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

The Common Centre of the Two Circles

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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

Tangents from an External Point to a Circle

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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

[]

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

Tangents from P to the Circle with Centre O

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Answer:

We know that the lengths of the tangents drawn form an external point to a circle are equal.