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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(student) , on 5/12/11

Answers

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

Posted by Navin Saxena(parent)on 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(student)on 5/12/11

Sorry the diagram is not coming...

Hope whatever I 've Answered will help you..

Posted by Bhavana Hegde(student)on 5/12/11

thanx for yor help.. ;)

Posted by Asma Afzal(student)on 9/12/11

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