A triangle is right-angled at and is drawn inside a circle so that all three vertices…

MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

A triangle

PQR

is right-angled at

Q

and is drawn inside a circle so that all three vertices lie on the circumference. The lengths of the perpendicular sides are

PQ = 8\,\text{cm}

and

QR = 15\,\text{cm}

. (i) Prove that

PR

is a diameter of the circle. (ii) Determine the radius of the circle. (iii) Calculate, correct to one decimal place, the area of the circle.