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if an isosceles triangle is inscribed in a circle and two sides have the length of 25 cm and base 14 cm what is the radius of the circle

Answer :

using heron's  formula,we know that Ar=root of [s(s-a)*(s-b)*(s-c)] where s=(a+b+c)/2 AND a,b and c are the measures of the sides
here,
Ar. of triangle= root of [32*7*7*18]=168
i.e. altitude*14=168
so, altitude=168/14=12
we know that - 'in an isosceles triangle altitude is also the median AND the center of the circle divides the median in to the ratio 2:1'
in this case 2x will be the radius of the circle
so,we get,
2x+x=12
3x=12
x=12/3=4
hence the radius of the circle=2x=8cm
 

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