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
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