Please wait...
1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days
For Business Enquiry


Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this toll free number


Mon to Sat - 11 AM to 8 PM

A tangent PT is drawn parallel to a chord AB of a circle. Prove that APB is an isosceles triangle.

Asked by 11th March 2013, 12:52 AM
Answered by Expert

Construction: Join PO and produce to D.

Now, OP is perpendicular TP  (tangent makes a 90 degree angle with the radius of the circle at the point of contact)

Also, TP is parallel to AB 

∴∠ADP=90° (corresponding angles)

So, OD is perpendicular to AB. Now since, a perpendicular drawn from the center of the circle

to a chord bisects it.

Hence, PD is a bisector of AB. i.e. AD = DB

Now in triangle ADP and BDP

AB =DB (proved above) 

∠ADP=∠BDP (both are 90°)

 PD = DP  (common)


Hence, ∠PAD = ∠PBD (By CPCT)

Thus, APB is an isosceles triangle.

Answered by Expert 11th March 2013, 4:13 AM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Your answer has been posted successfully!

Chat with us on WhatsApp