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 semi-circle 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

15^2-a^2 = 20^2-(25-a)^2

solve to get a=9, so b=16

So, r^2+9^2 = 15^2

r^2 = 225-81=144

area of semi-circle 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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