Mathematics

Problem

Points

P, Q,

and

R

lie on a circle. It is given that

\angle QPR = 90^{\circ}

and

PQ = 18\,\text{cm}

PR = 24\,\text{cm}

. What is the radius of the circle? a)

30\,\text{cm}

15\,\text{cm}

12\,\text{cm}

21\,\text{cm}

Intuitive explanation

When an inscribed angle is a right angle, it subtends a semicircle—meaning the side opposite that angle must be a diameter. Here, $\angle QPR = 90°$ tells you that $QR$ is a diameter. Use the Pythagorean theorem to find $QR$ from the two legs of the right triangle, then the radius is simply half the diameter.

Intuitive explanation

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