Geometry  semicircle inside isosceles triangle
posted by Knights .
Isosceles triangle ABC has sides of length AB=AC=25 and BC=40 . Find the area of a semicircle inscribed in triangle ABC with diameter along BC .
Please help I do not know how to start....

Geometry  semicircle inside isosceles triangle 
Steve
If the center of the semicircle is O, draw OD where D is the point where AC is tangent to o the circle.
Since OD┴AD, if the radius is r, let a=AD and b=DC, so a+b=25
r^2 + a^2 =15^2
r^2 + b^2 = 20^2
equating r^2, we get
15^2a^2 = 20^2(25a)^2
solve to get a=9, so b=16
So, r^2+9^2 = 15^2
r^2 = 22581=144
area of semicircle is 1/2 pi r^2 = 72pi 
Geometry  semicircle inside isosceles triangle 
Knights
Thanks a lot!

Geometry  semicircle inside isosceles triangle 
AOPS
Stop Cheating!

Geometry  semicircle inside isosceles triangle 
Overseer
Wow...AoPS caught you...don't know what to say...
However, it is still quite funny... 
Geometry  semicircle inside isosceles triangle 
AoPS
In violation of our honor code. The previous AoPS was an imposter, his username had an uppercase "O" instead of the correct lowercase o.

Geometry  semicircle inside isosceles triangle 
Anonymous
i agree and please ask for hints on the message boards. THe questions are supposed to be challenging try to solve them by yourself
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