Math CentralQuandaries & Queries


Question from NIHAL, a student:

A isosceles triangle is inscribed in a circle having sides 20cm,20cm,30cm. find the radius of circle


In my diagram $PQR$ is the isosceles triangle, C is the centre of the circle. Angle $QSP$ is a right angle. Can you see why?

inscribed triangle

Use the fact that triangle $QSP$ to find the length $|QS|.$

Suppose that $r$ is the radius of the circle and $|SC| = x.$ Use the fact that $|QC| = r = |QS| + |SC|$ and the fact that triangle $PSC$ is a right triangle to find $r.$


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