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Theorem:If two tangents are drawn to a circle from an external point ; then (i) they subtend equal angles at the centre. (ii) they are equally inclined to the line segments ; joining the centre to that point.

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If two tangents are drawn to a circle from an external point,then (i) they are equal (ii) they subtends equal angles at the centre.(iii) they are equally inclined to the segment; joining the centre to that point.

Equal chords of a circle subtend equal angles at the centre.

Knowledge Check

  • Choose the CORRECT option about the two tangents drawn to the circle from the external point? 1. The tangents subtend equal angles at the centre of the circle. 2. The tangents drawn from the external point to a circle are equal in length. 3. The tangents are equally inclined to the segment which joins the centre to that point.

    A
    1 and 2 only
    B
    2 and 3 only
    C
    1, 2 and 3
    D
    1 and 3 only

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    Explore conceptually related problems

    Assertion(A) If two tangents are drawn to a circle from an external point then they subtend equal angles at the centre. Reason (R ) A parallelogram circumscribing a circle is a rhombus

    Prove that equal chords of a circle subtend equal angles at the centre.

    Theorem: The length of two tangents drawn from an external point to a circle are equal.

    Equal chords of congruent circles subtend equal angles at the centre.

    Equal chords of congruent circles subtend equal angles at the centre.

    Theorem 10.1 : Equal chords of a circle subtend equal angles at the centre

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

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