Question

16. Let y be a circle with center O and let P, Q, and R be three points on y. Prove that if P and R are diametrically opposite, then $\angle PQR$ is a right angle, and if O and Q are on the same side of PR, then $$\angle PQR$^\circ = \frac{1}{2} (\angle POR)^\circ$. (Hint: Again use the fact that the triangu- lar angle sum is 180°. There are four cases to consider, as in Fig- ure 5.18.) State and prove the analogous result when O and Q are on opposite sides of PR.

          16. Let y be a circle with center O and let P, Q, and R be three points
on y. Prove that if P and R are diametrically opposite, then \(\angle PQR\)
is a right angle, and if O and Q are on the same side of PR, then
$\(\angle PQR\)^\circ = \frac{1}{2} (\angle POR)^\circ$. (Hint: Again use the fact that the triangu-
lar angle sum is 180°. There are four cases to consider, as in Fig-
ure 5.18.) State and prove the analogous result when O and Q are
on opposite sides of PR.

16. Let y be a circle with center O and let P, Q, and R be three points
on y. Prove that if P and R are diametrically opposite, then ∠ PQR
is a right angle, and if O and Q are on the same side of PR, then
∠ PQR^∘ = (1)/(2) (∠ POR)^∘. (Hint: Again use the fact that the triangu-
lar angle sum is 180°. There are four cases to consider, as in Fig-
ure 5.18.) State and prove the analogous result when O and Q are
on opposite sides of PR.

Added by Christopher C.

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