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.
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).
In triangle AOP,
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.
In triangle APB,
|AOP + |OAP + |APO = 1800
600 + 900 + |APO = 1800
|APO = 1800 – 1500
|APO = 300
|APB = 2|APO
|APB = 600
AP = BP
=> APB is an equilateral triangle.
Bhavana Hegde(student)on 5/12/11
Sorry the diagram is not coming...
Hope whatever I 've Answered will help you..
thanx for yor help.. ;)
Asma Afzal(student)on 9/12/11
sorry...it was ABP!