Question

A chord of length 6 cm is at a distance of 7.2 cm from the centre of a circle. Another chord of the same circle is of length 14.4 cm. Find its distance from the centre.

Answer 1

AF = FB = 3cm 

CE = ED = 7.2cm
(Perpendicular from centre to a chord bisects the chord) 

In right Δ AFO, By Pythagoras theorem, 

OA² =OF²+ AF² 

OA² = (7.2)² + (3)² 

OA² = 51.84 + 9 

OA² = 60.84 

OA = 7.8cm 

OA = OC = 7.8cm         (radii of same circle) 

Similarly, In right Δ OFC, 

OC² = OE² + EC² 

OE² = (7 .8)² - (7.2)² 

= 60.84 - 51.84 

OE² = 9 

OE = 3cm 

Distance from centre of chord CD with length 14.4cm is 3cm.