Question

10. 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 centre.​

Answer 1

Answer:

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

As radius of the circle is perpendicular to the tangent.

OA⊥PA

Similarly OB⊥PB

∠OBP=90 o

 

∠OAP=90 o

 

In Quadrilateral OAPB, sum of all interior angles =360 o

 

⇒∠OAP+∠OBP+∠BOA+∠APB=360  o

 ⇒90o+90o +∠BOA+∠APB=360 o

∠BOA+∠APB=180 o

 

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

hope it helps

tq./

Step-by-step explanation: