CBSE Class 10-Mathematics: Questions and Answers Chapter –10 Circles Part 17
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Question 17:
Two tangents TP and TQ are drawn to a circle with center O from an external point T. Prove that .

A Circle with Centre O
Answer:
Given: A circle with center O and an external point T and two tangents TP and TQ to the circle, where P and Q are the points of contact
To prove:
Proof: Let
In , we have
[Length of the tangents drawn from an external point to a circle are equal]
So, TPQ is an isosceles triangle.
In we have
But
[Angle between the tangent and radius of a circle is ]
Now
Question 18:
Prove that the parallelogram circumscribing a circle is a rhombus

ABCD be the Parallelogram
Answer:
Given: ABCD be the parallelogram circumscribing a circle with centre O such that the sides AB, BC, CD and DA touch a circle at P, Q, R and S, respectively.
To prove: is a rhombus.
Proof: …(i)
…(ii)
…(iii)
…(iv)
[Tangents drawn from an external point to a circle are equal]
Adding (i), (ii), (iii) and (iv), we get
Question 19:
Prove that the tangents drawn at the ends of a chord of a circle make equal angles with chord.

Tangents Drawn at the Ends of a Chord
Answer:
Let NM be chord of circle with center C.
Let tangents at M.N meet at the point O.
Since OM is a tangent
is a tangent
Again in
Thus, tangents make equal angle with the chord.