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Prove that the lengths of tangents drawn from an external point to a circle are equal.
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Prove that the lengths of tangents drawn from an external point to a circle are equal.
Given:
PT and QT are two tangent drawn from an external point T to the
circle C
To prove: PT = TQ
Construction: Join OT.
Proof:
We know that, a tangent to circle is perpendicular to the radius
through the point of contact.
∴ ∠OPT = ∠OQT = 90°
In ΔOPT and ΔOQT,
OT = OT (Common)
OP = OQ ( Radius of the circle)
∠OPT = ∠OQT (90°)
∴ ΔOPT ≈ ΔOQT (RHS congruence criterion and let ≈ equal to congruent)
⇒ PT = TQ (CPCT)
Thus, the lengths of the tangents drawn from an external point to a circle are
equal.
Hence Proved
☺☺☺ Hope this Helps ☺☺☺
Given:
PT and QT are two tangent drawn from an external point T to the
circle C
To prove: PT = TQ
Construction: Join OT.
Proof:
We know that, a tangent to circle is perpendicular to the radius
through the point of contact.
∴ ∠OPT = ∠OQT = 90°
In ΔOPT and ΔOQT,
OT = OT (Common)
OP = OQ ( Radius of the circle)
∠OPT = ∠OQT (90°)
∴ ΔOPT ≈ ΔOQT (RHS congruence criterion and let ≈ equal to congruent)
⇒ PT = TQ (CPCT)
Thus, the lengths of the tangents drawn from an external point to a circle are
equal.
Hence Proved
☺☺☺ Hope this Helps ☺☺☺
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