Question

two chords about and CD of lengths 24 CM and 10 CM respectively of a circle are parallel. if the chords and distance between them is 7 CM find the diameter if the circle ​

Answer 1

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.