CBSE Class 10-Mathematics: Questions and Answers Chapter – 10 Circles Part 11

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Question 29:

In the given figure, ABCD is a cyclic quadrilateral and PQ is a tangent to the circle at C. If BD is a diameter, and , find .

BD is a Diameter

BD is a Diameter

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Answer:

is a diameter

[Angle in the semi-circle]

Question 30:

Two chords AB and CD of a circle intersect each other at P outside the circle. If cm, and , find .

AB and CD of a Circle

AB and CD of a Circle

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Answer:

[length of tangent from P]

Question 31:

In the adjoining figure, if AD, AE, and BC are tangents to the circle at D, E and F respectively, then prove that .

tangents to the circle

Tangents to the Circle

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Answer:

Now

Question 32:

In figure, PA and PB are tangents from P to the circle with center O. R is a point on the circle, prove that .

Length of Tangents from an External Point

Length of Tangents from an External Point

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Answer:

Since length of tangents from an external point to a circle are equal in length

And

Now

Question 33:

The length of tangents from a point A at distance of from the centre of the circle is , what will be the radius of the circle?

The length of tangents from a point A

The Length of Tangents from a Point A

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Answer:

Since tangents to a circle is perpendicular to radius through the point of contact

In right , we have