CBSE Class 10-Mathematics: Questions and Answers Chapter –10 Circles Part 22

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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.

Two tangents are drawn to a circle

Two Tangents Are Drawn to a Circle

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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.