Question

2. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre 0 at a point Q so that OQ = 13 cm. Find length of PQ.​

Answer 1

(Diagram is given in attachment)

In the given question,

• PQ is a tangent
• O is the centre of circle

We know that

♦ OQ = 13 cm

♦ PO = 5 cm

Now,

In ∆OQP

By Tangent Perpendicularity Theorem,

∠OPQ = 90°

Applying Pythagoras theorem,

(OQ)² = (OP)² + (PQ)²

⇒ (13)² = (5)² + (PQ)²

⇒ 169 = 25 + (PQ)²

⇒ (PQ)² = 169 - 25

⇒ (PQ)² = 144

⇒ PQ = √144

⇒ PQ = ± 12 cm

Tangent cannot be negative.

So, PQ = 12 cm

Know more:

★ Tangent Perpendicularity Theorem states that radius always makes right angles (90°) with tangent.

★ 2 tangents drawn from a point to a circle are equal