AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, then the radius of the circle is _____.
A
14 cm
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B
10 cm
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C
13 cm
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D
15 cm
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Solution
The correct option is C 13 cm
Given AB and CD are two chords of a circles on opposite sides of the centre.
Construction: Draw perpendiculars OE and OF onto AB and CD respectively from centre O. AE = EB = 5cm and CF = FD = 12 cm [ Perpendicular drawn to a chord from center bisects the chord]
Given, Distance between two chords = 17 cm Let distance between O and F =x cm And distance between O and E =(17−x)cm
In ΔOEB, OB2=OE2+EB2 [Pythagoras theorem] =(17−x)2+52 ---(1)
In ΔOFD, OD2=OF2+FD2 [Pythagoras theorem] =(x)2+122----------→(2)
But OB = OD ( radii of the same circle).
From 1 & 2, (17−x)2+52=(x)2+122 ⇒ 289+x2−34x+25=x2+144 ⇒ 34x=170 ∴ x=5 Subsitute x in equation (2); OD2=(5)2+122=169 OD=13 ∴ Radius of the circle is 13 cm.