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Cryxone asked this question on Class X » Math » Circles

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..

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

Posted by navinsaxena.del...(parent), on 5/12/11

sorry...it was ABP!

Posted by Cryxone(student), on 9/12/11

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 bhavanah20(student), on 5/12/11

Sorry the diagram is not coming...

Posted by bhavanah20(student), on 5/12/11

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

Posted by bhavanah20(student), on 5/12/11

thanx for yor help.. ;)

Posted by Cryxone(student), on 9/12/11

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