Segma

Geometry Level 3

The figure shows a circular segment , the chord AC = 2L , B is the mid point of AC. BD = H , is the maximum height of the segment . if L = 5√2 and H = 5( 2 - √2 ) . Then the Area of the segment A , will be A = m ( π – n ) , find mn ?


The answer is 50.

Aziz Alasha by Aziz Alasha , 59, Sudan

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1 solution

Hassan Abdulla
Jan 23, 2018

from the figure above

R 2 = L 2 + ( R − H ) 2 R^{ 2 }=L^{ 2 }+\left( R-H \right) ^{2}

R = L 2 + H 2 2 H = 10 R=\frac{L^2+H^2}{2H}=10

θ = s i n − 1 ( 5 2 10 ) = 45 ° \theta = sin ^{ -1 }{\left( \frac{5\sqrt { 2 } }{10} \right)}=45°

so the triangle is right triangle

Area of the segment = A r e a o f c i r c l e 4 \frac{Area of circle}{4} - Area of triangle

Area of the segment = 25 π − 50 = 25 ( π − 2 ) 25 \pi - 50 = 25 ( \pi - 2 )

m=25 and n=2

mn = 50

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