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geometry

Expert replies
by sunilrawat » Fri Sep 09, 2011 10:04 am
Side AB of triangle ABC lies on the diameter of circle O as shown in the figure above. Half of the height to side AB equals 4/5 of the radius of the circle.
If the area of triangle ABC is 90, what is the closest approximation to the area of semicircle AOB?
35
45
88
180
350
Image

I didn't understand the question. What does the bolder part mean ?
Though I solved it like this:
Approximating area of part of the triangle inside the circle as (90/2), I chose the answer as 88
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Source: — Problem Solving |

by cans » Fri Sep 09, 2011 10:10 am
radius = 6. base of abc = 2r and h = 8r/5 (half height to AB = 4r/5)
thus area = (1/2)bh = 8* r^2 / 5 = 90 -> r = 5 * 3 /2 = 15/2
area of semicircle = pi* r^2 /2 = (22/7) (225/8) = 11*225 / 28 = 2475/28 around 88
IMO C
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by force5 » Fri Sep 09, 2011 10:19 am
that statement means- that if Height of the triangle is H and if R is the radius of the circle then

H/2 = 4/5R

also given is 1/2 AB *H= 90

where AB = 2R

substituting the values you will get R = 15/2
and area of semicircle approx 88
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