Question

The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm, from the centre, what is the distance of the other chord from the centre ?

Answer 1

Data: Chords of a circle are 6 cm. and 8 cm. are parallel. The smaller chord is at distance of 4 cm. from the centre. 

To Prove: Distance between bigger chord and centre = ? 

Construction : Join OA and OC. 

Proof: AB || CD, AB = 6 cm, CD = 8 cm. 

OP⊥CD, OQ⊥CD. 

In ∆OPA, ∠P = 90° 

∴ OA² = OP² + PA² (According to Pythagoras theorem) 

= (4)²+ (3)² = 16 + 9 

OA² = 25 

∴ OA = 5 cm. OA = OC = 5 cm. 

(radii of the same circle.) 

Now, in ∆OQC, 

OC² = OQ² + QC² (5)² = x² + (4)² 

25 = x² + 16 

x² = 25 – 16 = 9 

∴ x = √9

∴ x = 3 cm. 

∴ Bigger chord is at a distance of 3 cm. from the centre.