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Asked by Kanishka Tayal

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.

Answers(1)

Answer

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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