Question

Draw a circle with center $O$ and radius $6$ cm. Take a point $P$ outside the circle at a distance of $10$ cm from $O$. Draw tangents to the circle from point $P$. Let the tangents intersect the circle in points $A$ and $B$. Find the approximate value of $\angle OPB$.

• A. ${37}^o$
• B. ${53}^o$
• C. ${45}^o$
• D. None of these

Answer 1

The correct option is A ${37}^o$

$\angle OPB={37}^o$ (measurement)

Also, $OAPB$ is cyclic quadrilateral and $\angle AOP=\angle BOP$

also,

$\angle APO=\angle BPO\angle AOB+\angle APB={180}^{o}2\angle BOP+2\angle OPB={180}^{o}2\times 53+2\angle OPB={180}^o(\angle BOP={53}^o)2\angle OPB={74}^o\angle OPB={37}^o$