Question

Ab and cd are two parallel chords of a circle which are on opposite sides of the center such that ab=10cm,cd=24cm and the distance between ab and cd is 17 cm.Find the radius of the circle.

Answer 1

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 = 5subsitute x in (1 ) 0r (2) equations ∴ radius of the circle = 13.