Question

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

Answer 1

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

MON is one straight line.
Here
AM = `1/2`AB = 3 cm 
CN = `1/2`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

r² = x² + 16      ....(From(1))
r² = 9 + 16 = 25
r = 5 cm
Hence, the radius of the circle is 5 cm.