Question

ap and bp are tangents to the circle angle aop =30°then angle apb=​

Answer 1

Given :- AP and BP are tangents to the circle ∠AOP = 30° .

To Find :- ∠APB = ?

Solution :-

from image we can see that, In ∆OAP we have,

→ ∠OAP = 90° { Tangent is perpendicular to the radius at the circumference.}

→ ∠AOP = 30° (given)

so,

→ ∠OAP + ∠AOP + ∠OPA = 180° (By angle sum property.)

→ 90° + 30° + ∠OPA = 180°

→ 120° + ∠OPA = 180°

→ ∠OPA = 180° - 120°

→ ∠OPA = 60°

then,

→ ∠APB = 2 * ∠OPA = 2 * 60° = 120° (Ans.)

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Answer 2

Given : ap and bp are tangents to the circle angle aop =30°

To Find :  apb=​

Solution:

Quadrilateral  AOBP  

Sum of angles of Quadrilateral = 360°

∠AOB + ∠OAP  + ∠APB + ∠OBP  =   360°

∠OAP = ∠OBP = 90°  tangents

∠AOP =30°   => ∠AOB  = 2∠AOP = 2 *  30°  = 60°

=> 60° +90°  +   ∠APB + 90° = 360°

=> ∠APB = 120°

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