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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

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).

OM =OA

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

In APB,

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...

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

pleez..............

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

thanx for yor help.. ;)

Posted by Asma Afzalon 9/12/11

sorry...it was ABP!

Posted by Asma Afzalon 9/12/11