Find the length of the chord of a circle of diameter 34 cm which is at a distance of 8 cm from the centre of the circle.

Please help!

Question

Find the length of the chord of a circle of diameter 34 cm which
is at a distance of 8 cm from the centre of the circle
Please help!

Aakash Sharma · Accepted Answer

Let AB be the chord and OP be the distance of chord from the centre Then OP ⊥ AB

Given : Diameter = 34 cm

$\Rightarrow radius (OB) = \frac{Diameter}{2} = \frac{34}{2} cm = 17cm$

We know that perpendicular from the centre of the circle to the chord bisects the chord.

⇒ AP = BP

⇒ AB = AP + PB = PB + PB = 2 PB

Now In right ∆POB

OB² = OP² + PB² (Pythagoras theorem)

⇒ PB²= OB² – OP² = (17 cm)² – (8 cm)²= 289 cm² – 64 cm²= 225 cm²

$\Rightarrow PB = \sqrt{225} cm = 15 cm$

⇒ AB = 2 × 15 cm = 30 cm

Hence the length of the given chord is 30 cm.