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.
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.
Sorry the diagram is not coming...
Hope whatever I 've Answered will help you..
thanx for yor help.. ;)
sorry...it was ABP!