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..

#### Answers

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

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

Let m be the

In triangle AOP,

__ |A __ =90^{0}

M is the midpoint of the hypotenuse.

=> OA =

In triangle AOM,

OA =

=> AOM is equilateral triangle.

|__AOM__ =60^{0}

In triangle APB,

|__AOM__ =60^{0}

|__AOP__ + __|OAP__ + |__APO__ = 180^{0}

60^{0} + 90^{0} + __|APO__ = 180^{0}

|__APO__ = 180^{0} – 150^{0}

|__APO __= 30^{0}

|__APB__ = 2__|APO__

|__APB__ = 60^{0}

In APB,

AP = BP

|__APB__ = 60^{0}

=> APB is an equilateral triangle.

Sorry the diagram is not coming...

Hope whatever I 've Answered will help you..

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

thanx for yor help.. ;)

sorry...it was ABP!