AB and CD are two parallel chords of a circle such that AB =10cm and CD=24cm if chords are on opposite sides of the centre of the circle and distance between them is 17cm find the radius of circle
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Answer:
The correct option is D 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
)
c
m
In ΔOEB,
O
B
2
=
O
E
2
+
E
B
2
[Pythagoras theorem]
=
(
17
−
x
)
2
+
5
2
---(1)
In ΔOFD,
O
D
2
=
O
F
2
+
F
D
2
[Pythagoras theorem]
=
(
x
)
2
+
12
2
----------→(2)
But OB = OD ( radii of the same circle).
From 1 & 2,
(
17
−
x
)
2
+
5
2
=
(
x
)
2
+
12
2
⇒
289
+
x
2
−
34
x
+
25
=
x
2
+
144
⇒
34
x
=
170
∴
x
=
5
Subsitute x in equation (2);
O
D
2
=
(
5
)
2
+
12
2
=
169
O
D
=
13
∴ Radius of the circle is 13 cm.
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