CBSE Class 10-Mathematics: Questions and Answers Chapter –10 Circles Part 7
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Question 10:
Two concentric circles are of radii and . Find the length of the chord of the larger circle which touches the smaller circle.

The Common Centre of the Two Circles
Answer:
Let be the common centre of the two concentric circles.
Let AB be a chord of the larger circle which touches the smaller circle at .
Join and .
Then,
[The tangent at any point of a circle is to the radius through the point of contact
[By Pythagoras theorem]
Since the perpendicular from the center of a circle to a chord bisects the chord, therefore
Question 10:
A quadrilateral ABCD is drawn to circumscribe a circle (see figure). Prove that:

Tangents from an External Point to a Circle
Answer:
We know that the tangents from an external point to a circle are equal.
On adding eq. (i), (ii), (iii) and (iv), we get
Question 12:
In two concentric circles prove that all chords of the outer circle which touch the inner circle are of equal length.
Answer:
AB and CD are two chords of the circle which touch the inner circle at M and N.
Respectively
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Question 13:
PA and PB are tangents from P to the circle with center O. At the point M, a tangent is drawn cutting PA at K and PB at N. Prove that .

Tangents from P to the Circle with Centre O
Answer:
We know that the lengths of the tangents drawn form an external point to a circle are equal.