Question
Prove that the lengths of tangents drawn from an external point to a circle are equal.
Solution
Construction: Draw a circle centred at O.
Let PR and QR are tangent drawn from an external point R to the circle
touching at points P and Q respectively.
touching at points P and Q respectively.
Join OR.
Proof:
In ΔOPR and ΔOQR,
OP=OQ (Radii of the same circle)
∠OPR =∠OQR (Since PR and QR are tangents to the circle)
OR=OR (Common side)
Thus, tangent drawn from an external point to a circle are equal
Proof:
In ΔOPR and ΔOQR,
OP=OQ (Radii of the same circle)
∠OPR =∠OQR (Since PR and QR are tangents to the circle)
OR=OR (Common side)
Thus, tangent drawn from an external point to a circle are equal
