Question

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

Answer 1

Distance of smaller chord AB from centre of circle = 4 cm 

OM = 4 cm 

MB = \(\frac{AB}{2}\) = \(\frac{6}{2}\)

= 3 cm

In Δ OMB,

OM² + MB² = OB² 

(4)² + (3)² = OB² 

16 + 9 = OB² 

OB² = 25 

OB = 5 cm

In Δ OND,

OD = OB = 5 cm 

(Radii of same circle)

ND = \(\frac{CD}{2}\) = \(\frac{8}{2}\)

= 4 cm

ON² + ND² = OD² 

ON²+ (4)² = (5)² 

ON² = 25 – 16 = 9 

ON = 3 

So, 

Distance of bigger chord from circle is 3 cm.