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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 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 Î”OEB is an right angle traingle then

OB^{2} = OF^{2} + FD^{2}

= (17- x)^{2} + 5^{2} ----------â†’(1)

In a Î”OFD is an right angle traingle then

OD^{2} = OE^{2} + EB^{2}

= (x)^{2} + 12^{2} ----------â†’(2)

But OB = OD ( radius )

From 1 & 2

(17- x)^{2} + 5^{2} = (x)^{2} + 12^{2}

â‡’ 289 + x^{2} -34x +25 = x^{2 }+144

â‡’ 34x = 170

âˆ´ x = 5

subsitute x in (1 ) 0r (2) equations

âˆ´ radius of the circle = 13.

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 Î”OEB is an right angle traingle then

OB

= (17- x)

In a Î”OFD is an right angle traingle then

OD

= (x)

But OB = OD ( radius )

From 1 & 2

(17- x)

â‡’ 289 + x

â‡’ 34x = 170

âˆ´ x = 5

subsitute x in (1 ) 0r (2) equations

âˆ´ radius of the circle = 13.