Question
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....
Please help I do not know how to start....
Answers
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 ODâ”´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
Since ODâ”´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
Knights
Thanks a lot!
AOPS
Stop Cheating!
Overseer
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However, it is still quite funny...
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.
Anonymous
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AoPS
Ask for hints on the message boards instead of online. You are not benefitting yourself by asking for answers online.
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Richard Rusczyk
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Anonymous
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