Ab Cd Are Parallel Chords Of Circle 7 Cm Apart

AB, CD are parallel chords of a circle 7 cm apart. If AB = 6 cm, CD = 8 cm, find the radius of the circle.

Answers:

Let O be the centre of the circle OM and ON are perpendicular on AB and CD.

MON  is one straight line.

Here   AM = ½ AB = 3 cm, CN = ½ CD = 4 cm

Let   ON = x cm and radius  OA = OC = r cm

From right angled triangle OCN,  

ON² = OC² – CN²    [By Pythagoras Theorem]

x² = r² – 16   ….(1)

From right angled triangle OAM,

OM² = OA² – AM²   [By Pythagoras Theorem]

(7 – x)² = r² – 9      …..(2)

From (1) and (2)

(7 – x)² – x² = 7

49 + x² – 14x – x² = 7

14x = 42

x = 3

from (1),    r² = x² + 16

= 9 + 16 = 25

r = 5 cm

Hence, the radius of the circle is 5 cm.