Question

In the $△$PQR, find $\angle$PCQ where C is the circumcenter of $△$PQR.

• A. ${75}^{\circ }$
• B. ${120}^{\circ }$
• C. ${90}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is D

${60}^{\circ }$

The angle subtended by the chord PQ at the circumference = ${30}^{\circ }$

The angle subtended by the chord at the center is twice the angle subtended by the chord at the circumference. (In the same segment)

PQ is a chord subtending ${30}^{\circ }$ at R, which is on the circumference. Therefore it should subtend twice of this angle at the center C.

Therefore $\angle PCQ=2\times {30}^{\circ }={60}^{\circ }$