Question

AB and CD are parallel chords on opposite sides of centre of circle. If AB = 10 cm, CD = 24 cm, distance between chords is 17 cm, radius of circle is

• A. 10 cm
• B. 13 cm
• C. 15 cm

Answer 1

The correct option is B 13 cm


Given: AB and CD are parallel chords on opposite sides of the centre of a circle.
Distance between two chords = 17 cm

Construction:
Draw perpendiculars OE and OF onto AB and CD respectively from centre O.

AE = EB = 5 cm and CF = FD = 12 cm

[Perpendicular drawn to a chord from the centre bisects the chord]


Let distance between O and F $=x$ cm
So, distance between O and E $=(17-x)cm$

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,
$(17-x{)}^2+5^2=(x{)}^2+{12}^2$
⇒ $289+x^2-34x+25=x^2+144$
⇒ $34x=170$
∴ $x=5$
Subsitute x in equation (2);
$O{D}^2=(5{)}^2+{12}^2=169$
$OD=13$
∴ Radius of the circle is 13 cm.