You are doing a very good job. Keep it up. Subscribed your channel. 👍
@ronney6121Күн бұрын
I have a passion for geometry. I solved it in 2 minutes. 😎
@ashokgupta310Күн бұрын
Very beautiful question
@hklrao2 күн бұрын
Please listen to the wonderful and motivating address of Prime Minister Modiji on Olympied Mathematics day and his conversation with high rank Maths students and get motivated to learn and promote Maths Dr.LakshmanRao PhD Krishnapuŕi Chennai 600 028
@starlordplays12062 күн бұрын
Add the area of quarter and semi circle
@Shri_123563 күн бұрын
Semi circle and quarter circle ke area ko ek dusre me add karna tha minus nahi 👎🏻
@anandharamang32894 күн бұрын
BE /AB = tan 30 =1/√3 BE= AB/√3= 10/√3 Red Area = 1/2 *AB*(AD+(BC-BE)) = 1/2 * 10*(10+(10-10/√3)) =5*20-50/√3 = 100-50√3/3 =71.132 sq.u
@anandharamang32894 күн бұрын
Draw reflection below and make it a semi circle. Then we will get three points on the circle. Join to make a triangle with sides √12^2+16^2 , 9+9, √(12+9+9)^2+16^2 Sides calculated are 20,18, 34 Radius= abc/4∆, ∆ = 1/2*(9+9)*16 =144 Radius= 20*18*34/(4*144 )= 85/4=21.5 u
@pas62954 күн бұрын
21 units
@DR-kz9li4 күн бұрын
15=(9-r)+(12-4r) r=2
@ronney61213 күн бұрын
r = 6/5 aa rha hai
@prossvay874411 күн бұрын
Answer is 26.44
@erwinkurniadi185012 күн бұрын
This is an example of a difficult way to solve it, even though there are other easy ways
@markandeysingh135513 күн бұрын
How to solve by Geometry, not Trignometry ?
@prossvay874413 күн бұрын
Red area=1/2(12)(6√5)=36√5=80.50
@prossvay874413 күн бұрын
Quarter area=1/4(π)(√10/2)^2=5π/8=1.96 square units
@bpark1000113 күн бұрын
What are you doing?!!!! You only need to translate the segments to form a right triangle 6/8/? AB = √(6² + 8²) = √(36 + 64) = √(100) = 10.
@ashwinbapat14 күн бұрын
sir +class 10 coordinate geometry ke questions bata digiay
@JangiLalPatel-wd4do15 күн бұрын
It is not easy way to solve
@sorourhashemi324916 күн бұрын
Thanks. You did great. My problem is I don't know anything about cos. is it possible to be solved the other way?
@amitavadasgupta698516 күн бұрын
ar of tr.=4×3/2=6 unit=6r when r is radius of inscribed circle.=>r=1 unit make ar of circle=pai.r^1=pai.1=pai when pai=22/7.proved
@amitavadasgupta698516 күн бұрын
AB=(6^2+8^2)^1/2=(36+64)^1/2=100^1/2=10 Unit.ans
@salimahmad741416 күн бұрын
AB = 10 units of length.
@erwinkurniadi185018 күн бұрын
15 x 15 = 36 x BD BD = 6.25 diameter = 36 + 6.25 = 42.25 radius = 21.125 area of the circle = π 21.125² area = 1401.274 cm²
@lasalleman679220 күн бұрын
Find inradius first. Inradius is = to the area of the triangle /semi-perimeter. Here, area of triangle 54/semi-perimeter of 18 = inradius of 3 . Area of circle is thus PI * 3^2 = Area of circle 28.2743.
@ManojkantSamal21 күн бұрын
Given l=13 I found out b=60/13 Area =l×b=13×(60/13)=60 Let BE=x So,AE=13-x In triangle ADE AD^2=12^2-(13-x)^2 =144-(169+x^2-26x) =144-169-x^2+26x In triangle BCE BC^2=5^2-x^2 =25-x^2 We know BC=AD SO, 144-169-x^2+26x=25-x^2 -25+26x=25 26x=50 X=50/26=25/13 In triangle BCE BC^2=25-x^2 =25-(25/13)^2 =25-(625/169) ={(169×25)-625}/169 ={25(169-25)}/169 =(25×144)/169 BC=(5×12)/13 =60/13 Area of rectangle =CD×BC =13×(60/13)=60.... Respected Sir,pranam... I prefer the way your answering
@krishnaswamyv-nb5zh21 күн бұрын
S
@krishnaswamyv-nb5zh21 күн бұрын
IS ANGLE DEC IS 90.’
@MeenakshiSinha-dc6uu24 күн бұрын
Sir 2.77-1 =1.77 not 2.76. So sorry
@sreenathreddy917324 күн бұрын
Triangle EDC and Triangle BEC are similar triangles by Angle Angle Angle. that means BC/12 = 5/13 BC = 60/13... Area of rectanlge = BC * AB = 60 S.Units
@amitavadasgupta698524 күн бұрын
ar of rt triangle=12×5/2=30 sq unit.
@amitavadasgupta698524 күн бұрын
ar. of rectangle=2×ar.of triangle with same base and same parallel.=2×30=60 sq unit.ans
@santokhsidhuatla704524 күн бұрын
Let h is height of Rectangle 12^2-h^2+5^-h^2=13 144+25-13=h^+h^2 156 =2h^2 h=156/2=78^1/2 Area of Rectangle =13 * 78^1/2 =114.813 square units
@mariocohen581625 күн бұрын
This triangle is rectangular because 13^ 2=12^2+5^2 thus Area (5×12):2=30square unit
@mariocohen581625 күн бұрын
We also have if h is the height of triangle relative to the base 13 this height is also the wish of there rectangle since the triangle is rectangular we have the relation 13×h=12×5 h=4,615.Thus Area Rectangle= 4,615×13=60
@sorourhashemi324925 күн бұрын
Area of Triangle=30 square units by Heroin F. Height or width= 4.66 area ofrectangle=60 square units
@AbdulJaleel-rd5ul25 күн бұрын
Area of triangle 30 square unit. So area of rectangle is double double of that.
@plamenpenchev26226 күн бұрын
Square side = 2a, chord theorem: 2×(2a) = a^2, a = 0, a = 4 Then 2r = 2×4 +2, r = 5
@AtharvaAgarwal27 күн бұрын
This is olympiad? Its easier than my school
@joysebastianpoovakulam710228 күн бұрын
wrong, i feel answer is 25.12
@sorourhashemi324928 күн бұрын
Heron result is radical 720; so the area is 26.832. And area of red semi circle 17.242
@amitavadasgupta698529 күн бұрын
ar=4.5 pai.(pai=22/7)
@amitavadasgupta698529 күн бұрын
BD=10-6=4
@santokhsidhuatla7045Ай бұрын
Side of square =a= Ur2xa=10xur2 a=10 Area of square =10x10=100 su Srea of circle=pi/4x100=78.5 su Net area=100-78.5=21.5su Read shaded area=21.5/4=5.375sq unit
@PrithwirajSen-nj6qqАй бұрын
Red area and other three each of the same shaped areas are equal -- it has been said without any logic. This may be discussed also to make the solution a clear one
@peterotto712Ай бұрын
It would be interesting to learn what language you are talking
@AbhayPratapSinghRajawat-ch4uzАй бұрын
but it is is not ,GIVEN THAT DIAGONAL OF SQUARE PASSES THROUGH CENTER OF CIRCLE or RADII JOINING VERITICE OF SMALL AND BIG SQUARE FORM A LINE
@deviprasad8993Ай бұрын
Why centre of circle and small square are collinear.
@ashwinbapatАй бұрын
bhohat sahi sir maja aa gaya .
@OverclockingCowboyАй бұрын
Another problem wherein the red area is not dependent on the radius of the circles with radius R, (R+r)/2, and r.
I solved the same way. But a minute later: As inspected, the area does not depend on three radii. This means that you can make upper semi-circle with r = 0 and obtained a semi-circle (red) with diameter 12. Then S = pi*6^2/2 = 18×pi.
@OverclockingCowboyАй бұрын
Yeah, the red area is constant regardless of the value of r ( r = 6-x ).
Пікірлер
You are doing a very good job. Keep it up. Subscribed your channel. 👍
I have a passion for geometry. I solved it in 2 minutes. 😎
Very beautiful question
Please listen to the wonderful and motivating address of Prime Minister Modiji on Olympied Mathematics day and his conversation with high rank Maths students and get motivated to learn and promote Maths Dr.LakshmanRao PhD Krishnapuŕi Chennai 600 028
Add the area of quarter and semi circle
Semi circle and quarter circle ke area ko ek dusre me add karna tha minus nahi 👎🏻
BE /AB = tan 30 =1/√3 BE= AB/√3= 10/√3 Red Area = 1/2 *AB*(AD+(BC-BE)) = 1/2 * 10*(10+(10-10/√3)) =5*20-50/√3 = 100-50√3/3 =71.132 sq.u
Draw reflection below and make it a semi circle. Then we will get three points on the circle. Join to make a triangle with sides √12^2+16^2 , 9+9, √(12+9+9)^2+16^2 Sides calculated are 20,18, 34 Radius= abc/4∆, ∆ = 1/2*(9+9)*16 =144 Radius= 20*18*34/(4*144 )= 85/4=21.5 u
21 units
15=(9-r)+(12-4r) r=2
r = 6/5 aa rha hai
Answer is 26.44
This is an example of a difficult way to solve it, even though there are other easy ways
How to solve by Geometry, not Trignometry ?
Red area=1/2(12)(6√5)=36√5=80.50
Quarter area=1/4(π)(√10/2)^2=5π/8=1.96 square units
What are you doing?!!!! You only need to translate the segments to form a right triangle 6/8/? AB = √(6² + 8²) = √(36 + 64) = √(100) = 10.
sir +class 10 coordinate geometry ke questions bata digiay
It is not easy way to solve
Thanks. You did great. My problem is I don't know anything about cos. is it possible to be solved the other way?
ar of tr.=4×3/2=6 unit=6r when r is radius of inscribed circle.=>r=1 unit make ar of circle=pai.r^1=pai.1=pai when pai=22/7.proved
AB=(6^2+8^2)^1/2=(36+64)^1/2=100^1/2=10 Unit.ans
AB = 10 units of length.
15 x 15 = 36 x BD BD = 6.25 diameter = 36 + 6.25 = 42.25 radius = 21.125 area of the circle = π 21.125² area = 1401.274 cm²
Find inradius first. Inradius is = to the area of the triangle /semi-perimeter. Here, area of triangle 54/semi-perimeter of 18 = inradius of 3 . Area of circle is thus PI * 3^2 = Area of circle 28.2743.
Given l=13 I found out b=60/13 Area =l×b=13×(60/13)=60 Let BE=x So,AE=13-x In triangle ADE AD^2=12^2-(13-x)^2 =144-(169+x^2-26x) =144-169-x^2+26x In triangle BCE BC^2=5^2-x^2 =25-x^2 We know BC=AD SO, 144-169-x^2+26x=25-x^2 -25+26x=25 26x=50 X=50/26=25/13 In triangle BCE BC^2=25-x^2 =25-(25/13)^2 =25-(625/169) ={(169×25)-625}/169 ={25(169-25)}/169 =(25×144)/169 BC=(5×12)/13 =60/13 Area of rectangle =CD×BC =13×(60/13)=60.... Respected Sir,pranam... I prefer the way your answering
S
IS ANGLE DEC IS 90.’
Sir 2.77-1 =1.77 not 2.76. So sorry
Triangle EDC and Triangle BEC are similar triangles by Angle Angle Angle. that means BC/12 = 5/13 BC = 60/13... Area of rectanlge = BC * AB = 60 S.Units
ar of rt triangle=12×5/2=30 sq unit.
ar. of rectangle=2×ar.of triangle with same base and same parallel.=2×30=60 sq unit.ans
Let h is height of Rectangle 12^2-h^2+5^-h^2=13 144+25-13=h^+h^2 156 =2h^2 h=156/2=78^1/2 Area of Rectangle =13 * 78^1/2 =114.813 square units
This triangle is rectangular because 13^ 2=12^2+5^2 thus Area (5×12):2=30square unit
We also have if h is the height of triangle relative to the base 13 this height is also the wish of there rectangle since the triangle is rectangular we have the relation 13×h=12×5 h=4,615.Thus Area Rectangle= 4,615×13=60
Area of Triangle=30 square units by Heroin F. Height or width= 4.66 area ofrectangle=60 square units
Area of triangle 30 square unit. So area of rectangle is double double of that.
Square side = 2a, chord theorem: 2×(2a) = a^2, a = 0, a = 4 Then 2r = 2×4 +2, r = 5
This is olympiad? Its easier than my school
wrong, i feel answer is 25.12
Heron result is radical 720; so the area is 26.832. And area of red semi circle 17.242
ar=4.5 pai.(pai=22/7)
BD=10-6=4
Side of square =a= Ur2xa=10xur2 a=10 Area of square =10x10=100 su Srea of circle=pi/4x100=78.5 su Net area=100-78.5=21.5su Read shaded area=21.5/4=5.375sq unit
Red area and other three each of the same shaped areas are equal -- it has been said without any logic. This may be discussed also to make the solution a clear one
It would be interesting to learn what language you are talking
but it is is not ,GIVEN THAT DIAGONAL OF SQUARE PASSES THROUGH CENTER OF CIRCLE or RADII JOINING VERITICE OF SMALL AND BIG SQUARE FORM A LINE
Why centre of circle and small square are collinear.
bhohat sahi sir maja aa gaya .
Another problem wherein the red area is not dependent on the radius of the circles with radius R, (R+r)/2, and r.
+CircleQuarter(r) = п/4 * 8² = 16п +CircleQuarter(r/2) = 16п/4 = 4п - CircleQuarter(r/4)*2 = 2*4п/4 = -2п RedArea = 16п + 4п - 2п = 18п
I solved the same way. But a minute later: As inspected, the area does not depend on three radii. This means that you can make upper semi-circle with r = 0 and obtained a semi-circle (red) with diameter 12. Then S = pi*6^2/2 = 18×pi.
Yeah, the red area is constant regardless of the value of r ( r = 6-x ).