Question

In the given figure 2, O is the centre of the circle with $\angle TQM={35}^{\circ }$ , then angle ATQ would be equal to :

• A. ${55}^{\circ }$
• B. ${56}^{\circ }$
• C. ${35}^{\circ }$
• D. ${54}^{\circ }$

Answer 1

The correct option is A ${55}^{\circ }$

In $△OTQ,OT=OQ....radii\Rightarrow \angle OTQ=\angle OQT={35}^o$

Tangent is perpendicular to radius at the point of contact. So

$\angle ATO=\angle ATQ+\angle OTQ={90}^o$

$\Rightarrow \angle ATQ=90-35={55}^o$

So option A is the right answer.