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From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is equal to the diameter of the circle, prove that triangle ABC is equilateral..


i really need the answer..my exams are starting tomorrow..

Asked by Asma Afzal , on 5/12/11

now what is "c" point in your question, is not explained.

Posted by Navin Saxenaon 5/12/11

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If your question is to show that triangle ABP is equilateral,

Let m be the mid-point of OP .i.e., M lies on the circle. (Since OP is equal to the diameter).



In triangle AOP,

|A =900

M is the midpoint of the hypotenuse.

=> OA = OM = AM (Mid-point of the hypotenuse is equidistant from all the vertices).

In triangle AOM,

OA = OM =AM.

=> AOM is equilateral triangle.

|AOM =600


In triangle APB,

|AOM =600


|AOP + |OAP + |APO = 1800

600 + 900 + |APO = 1800

  |APO = 1800 – 1500

  |APO = 300

|APB = 2|APO

|APB = 600



 AP = BP

|APB = 600

=> APB is an equilateral triangle.


Posted by Bhavana Hegde(Vidhya Ashram) on 5/12/11

 Sorry the diagram is not coming...

Hope whatever I 've  Answered will help you..

Posted by Bhavana Hegde(Vidhya Ashram) on 5/12/11

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