Posted by Knights on Thursday, March 21, 2013 at 2:14pm.
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, Thursday, March 21, 2013 at 2:49pm
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, Thursday, March 21, 2013 at 4:50pm
Thanks a lot!
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