Question

In the given figure, TAS is a tangent to the circle, with centre O, at the point A. If $\angle$OBA = ${32}^{\circ }$, find the value of x.

Answer 1

OB = OA (radius)

=>$\angle$OAB = $\angle$OBA = ${32}^{\circ }$

As the tangent at any point of a circle is perpendicular to the radius through the point of contact,

$\angle$OAS = ${90}^{\circ }$

x= $\angle$OAS - $\angle$OAB

x = ${90}^{\circ }$ - ${32}^{\circ }$

x = ${58}^{\circ }$