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
Related Questions
- In the adjoining figure, PT is a tangent at T to the circle with centre O. If $ \angle TPO = 30^o $, find the value of x
- Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord
- Assertion (A): A tangent to a circle is perpendicular to the radius through the point of contact
- The length of the arc of a circle of radius 14 cm which subtends an angle of
- How many tangents can be drawn to a circle from a point on it
- If the angle between two tangents drawn from an external point P to a circle of radius a and centre O