Question

The triangle PQR is inscribed in the circle $x ^ { 2 } + y ^ { 2 } = 25$. If Q and R have co-ordinates (3,4) and (– 4, 3) respectively, then $\angle Q P R$ is equal to.

• A. $\frac { \pi } { 2 }$
• B. $\frac { \pi } { 3 }$
• C. $\frac { \pi } { 4 }$
• D. $\frac { \pi } { 6 }$

Answer 1

Answer: (C)

$\frac { \pi } { 4 }$

Answer 2

Here the centre . So ‘m’ of OQ is $\frac { 4 } { 3 }$and ‘m’ of OR is $\frac { - 3 } { 4 }$, ∴ $\angle Q O R = \frac { \pi } { 2 }$

Hence $\angle Q P R = \frac { 1 } { 2 } \times \frac { \pi } { 2 } = \frac { \pi } { 4 }$ .