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 _____.
13
Open in App
Solution
The correct option is A 13
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.