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Important Questions

Circles

Editorially selected priority revision questions for this chapter.

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Important Questions

5

Q2

Hard Concept

State and prove Theorem 10.1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Q3

Hard Concept

State and prove Theorem 10.2: The lengths of tangents drawn from an external point to a circle are equal.

Q5

Hard Concept

Prove that in two concentric circles, the chord of the larger circle which touches the smaller circle is bisected at the point of contact.

Q6

Hard Concept

Two tangents $TP$ and $TQ$ are drawn to a circle with centre $O$ from an external point $T$ . Prove that $\angle PTQ = 2\angle OPQ$ .

Q7

Long Answer (5 Marks)

$PQ$ is a chord of length $8\text{ cm}$ of a circle of radius $5\text{ cm}$ . The tangents at $P$ and $Q$ intersect at a point $T$ . Find the length $TP$ .

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