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triangle ABC

by shashank.ism » Tue Feb 09, 2010 1:14 pm
In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

17.05
27.85
22.45
32.25
26.25
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by fibbonnaci » Wed Feb 10, 2010 12:39 am
there is a formula involved here which GMAT takers might not be familiar.
area of a triangle = (abc)/4R
where R = circumradius. a,b,c represent sides of the triangle.

Let a = AB, b = AC, c= BC

area of triangle ABC= abc/4R
also we know that area of triangle is 1/2 * base *height

=> 1/2 * c* 3

abc/4R = 1/2 * c *3

R= a*b/2*3 => 17.5 * 9/ 2* 3 => 26.25
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