CBSE Class 10-Mathematics: Questions and Answers Chapter – 10 Circles Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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.

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:

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.

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 .