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

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Solution

OB = OA (radius)

=> $∠$ OAB = $∠$ OBA = $32^{\circ}$

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

$∠$ OAS = $90^{\circ}$

x= $∠$ OAS - $∠$ OAB

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

x = $58^{\circ}$

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In the given figure, TAS is a tangent to the circle, with centre O, at the point A. If ∠OBA = 32∘, find the value of x.

OB = OA (radius) =>∠OAB = ∠OBA = 32∘ As the tangent at any point of a circle is perpendicular to the radius through the point of contact, ∠OAS = 90∘ x= ∠OAS - ∠OAB x = 90∘ - 32∘ x = 58∘

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

OB = OA (radius)

=> $∠$ OAB = $∠$ OBA = $32^{\circ}$

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

$∠$ OAS = $90^{\circ}$

x= $∠$ OAS - $∠$ OAB

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

x = $58^{\circ}$