CBSE Class 10-Mathematics: Questions and Answers Chapter –10 Circles Part 22
Get top class preparation for CBSE right from your home: fully solved questions with step-by-step explanation- practice your way to success.
Question 7:
From a point P two tangents are drawn to a circle with center . If diameter of the circle, show that is equilateral.

Two Tangents Are Drawn to a Circle
Loading image•••
Answer:
Join OP.
Suppose OP meets the circle at Q. Join AQ.
We have
i.e., diameter
diameter
Diameter – radius
Thus, radius
Thus, OP is the hypotenuse of right triangle
and is the mid-point of OP
[mid-point of hypotenuse of a right triangle is equidistant from the vertices]
is equilateral
So,
Also
But
Hence, is equilateral.