1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

022-62211530

Mon to Sat - 11 AM to 8 PM

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.

Asked by Topperlearning User 4th June 2014, 1:23 PM

Let us consider a circle centred at point O. Let P be a external point from which two tangents PA and PB are drawn to circle which are touching circle at point A and B respectively and AB is the line segment, joining point of contacts A and B together such that it subtends AOB at centre O of circle.

Now we may observe that:

So, OAP = 90o

OBP = 90o

Now in quadrilateral OAPB, sum of all interior angles = 360o

OAP + APB + PBO +BOA = 360o

90o + APB + 90o + BOA = 360o

APB +BOA = 180o

Hence, 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.

Answered by Expert 4th June 2014, 3:23 PM
• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10

You have rated this answer /10