Asked 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....
Answered by Steve
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
Answered by Knights
Thanks a lot!
Answered by AOPS
Stop Cheating!
Answered by Overseer
Wow...AoPS caught you...don't know what to say...

However, it is still quite funny...
Answered by 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.
Answered by 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
Answered by AoPS
Ask for hints on the message boards instead of online. You are not benefitting yourself by asking for answers online.
Answered by JEFF
MYNAMEJEFF
Answered by Richard Rusczyk
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Answered by Richard Rusczyk
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Answered by aops real one 100%
stop cheating



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Answered by Anonymous
facts tho
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