CBSE Class 10-Mathematics: Questions and Answers Chapter – 10 Circles Part 22 (For CBSE, ICSE, IAS, NET, NRA 2023)
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Question 7:
From a point P two tangents are drawn to a circle with center . If diameter of the circle, show that is equilateral.
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.