Prove that the lengths of tangents drawn from an external point to a circle are equal

Circles (10)

Prove that the lengths of tangents drawn from an external point to a circle are equal.

  • Answer:

    Given: A circle with centre O and PQ, PR are tangents to the circle from an external point P.

    To Prove: PQ = PR

    Construction: Join OP, OQ, OR

    Proof: In ΔOPQ and ΔOPR

    OP = OP (common)

    OQ = OR (radii of the same circle)

    ∠OQP = ∠ORP (each 90°)

    ΔPOQ ≅ ΔPOR (RHS congruence)

    PQ = PR
  • Exam Year: 2023