Question

chord ab//chordcd such that ab=24 cd=10 find distance between the 2 chords

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.