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!

## Answer This Question

## Related Questions

- Geometry - ABC is a right angled triangle with ∠ABC=90∘ and side ...
- Math (Geometry) - The perimeter of right triangle ABC is equal to the perimeter ...
- Maths - ABC is a right angled triangle with ∠ABC=90∘ and side ...
- Geometry - Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are...
- 9th grade - given that a(-1,8) ,b(2,4) and if the line y=4 is the axis of ...
- geometry!!!!!! - ABC is an isosceles triangle with AB = BC. The circumcircle of ...
- Geometry - Please answer at least one . PLEASE 1. Triangle XYZ has a right ...
- geometry - how do you find the height of an isosceles triangle only knowing the ...
- geometry - The perimeter of right triangle RST is equal to the perimeter of ...
- Geometry - Can anybody help me with this word problem? A homeowner, who loves ...

More Related Questions