Question

In Figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If $\angle POQ={70}^{\circ }$, then $\angle TPQ$ is equal to

• A. ${55}^{\circ }$
• B. ${70}^{\circ }$
• C. ${45}^{\circ }$
• D. ${35}^{\circ }$

Answer 1

Answer: (D)

${35}^{\circ }$

In $△OPQ,OP=OQ\Rightarrow \angle OPQ=\angle OQP$

$\angle POQ={70}^o\Rightarrow \angle OPQ=\angle OQP=\frac{180-70}{2}={55}^o$.

Since tangent is perpendicular to radius at the point of contact, we have:

$\angle OPT=\angle OPQ+\angle TPQ={90}^o\Rightarrow \angle TPQ=90-55={35}^o$.

So option D is the right answer.