Question

AB and CD are two parallel chords of a circle which are on the opposite sides of the centre such that AB = 16 cm , C D =12 cm and the distance between AB and CD is 14 cm. Find the radius of the circle.

Answer 1

Answer:

Given AB and CD are two chords of a circles D and E are midpoints of AB ,CD respectively.

CD = DB = 12 cm and AE = EB = 5 cm

Distance between two chords = 17 cm

Distance between  O and F = x cm

Distance between  O and E = (17- x) cm

In a ΔOEB   is an right angle traingle then

OB2 = OF2 + FD2

      = (17- x)2 + 52 ----------→(1)

In a ΔOFD is an right angle traingle then

OD2 = OE2 + EB2

      = (x)2 + 122 ----------→(2)

But OB = OD ( radius )

From 1 & 2

(17- x)2 + 52 = (x)2 + 122

⇒ 289 + x2 -34x +25 = x2 +144

⇒ 34x = 170

∴ x = 5

subsitute x in (1 ) 0r (2) equations

∴ radius of the circle = 13.

Step-by-step explanation: