Question

If tangents $TA$ and $TB$ from a point $T$ to a circle with centre $O$ are inclined to each other at an angle of ${70}^{\circ }$, then find $\angle AOB$ (in degrees).

Answer 1

Given:

$TA$ and $TB$ are tangents to circle $O$.

$\angle T={70}^o$

To find:

$\angle AOB$

Solution:

Tangent and normal at a point on a circle are perpendicular to each other.

$\angle A=\angle B={90}^o$

Sum of angles of a quadrilateral is ${360}^o$.

$\angle A+\angle B+\angle O+\angle T={360}^o$

${90}^o+{90}^o+\angle O+{70}^o={360}^o$

$\angle O={110}^o$