Question

Prove that the angle between the two tangents drawn from an external point to a circle is

supplementary to the angle subtended by the line-segment joining the points of contact at the

center.​

Answer 1

Answer:

Step-by-step explanation:

Draw a circle with center O and take an external point P. PA and PB are the tangents.

As the radius of the circle is perpendicular to the tangent. So,  

OA⊥PA

Similarly, OB⊥PB

∠OBP=90°  

∠OAP=90°  

In Quadrilateral OAPB, the sum of all interior angles =360°

 

⇒∠OAP+∠OBP+∠BOA+∠APB = 360°  

   

⇒90 +90  +∠BOA+∠APB = 360°  

 

∠BOA+∠APB = 180°  

 

It proves the angle between the two tangents drawn from an external point to a circle supplementary to the angle subtended by the line segment.