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..

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.

 Sorry the diagram is not coming...

Hope whatever I've  Answered will help you..

  pleez..............

thanx for yor help.. ;)