icse maths mensuration question

Subject: Re: icse maths mensuration question Thu Jul 03, 2008 4:25 pm

Is angle C = 90 degrees ?

AC = 1/2
BC = AB*cos(30) = sqrt(3)/2

So the area of the triangle is (1/2)*(1/2)*sqrt(3)/2 = sqrt(3)/8

The area of the triangle can also be expressed as:
(r*AB + r*AC + r*BC)/2 = r(AB + AC + BC) = (1 + 1/2 + sqrt(3)/2)r

So
(1 + 1/2 + sqrt(3)/2)r = sqrt(3)/8

r(3 + sqrt(3))/2 = sqrt(3)/8

r = sqrt(3)/[4(3 + sqrt(3)]
= 1/[4(sqrt(3) + 1)
= [sqrt(3) - 1]/4(3 - 1)
= [sqrt(3) - 1]/8