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Mar 1, 2014

# AB and CD are 2 parallel chords of a circle such that AB=10cm CD =24cm if 2 chords are on the opp side of the centre and the distance bw them is 17cm find the radius of

AB and CD are 2 parallel chords of a circle such that AB=10cm CD =24cm   if  2 chords are on the opp side of the centre  and the distance b/w them is  17cm    find the radius of circle.

Raghunath Reddy

Member since Apr 11, 2014

Sol : 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.
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