Question : The lengths of two parallel chords of a circle are 10 cm and 24 cm lie on the opposite sides of the centre. If the smaller chord is 12 cm from the centre, what is the distance (in cm ) between the two chords?
Option 1: 13
Option 2: 5
Option 3: 17
Option 4: 12
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Correct Answer: 17
Solution :
Let the length of ON be $x$ cm.
Distance between the two chords = $(12 +x)$ cm
AO, OB, OC, and OD are the radius of the circle.
In $\triangle AOM$,
$AO^2=AM^2+MO^2$
⇒ $AO^2=5^2+12^2$
⇒ $AO^2=25+144$
⇒ $AO^2=169$
⇒ $AO=\sqrt{169}$
⇒ $AO=13$ cm
⇒ $OC = 13$ cm
Now, In $\triangle CON$,
$OC^2=CN^2+ON^2$
⇒ $13^2=12^2+x^2$
⇒ $169-144=x^2$
⇒ $x = \sqrt{25}$
⇒ $x = 5$ cm
$\therefore$ Distance between two chords = (12 + 5) cm = 17 cm
Hence, the correct answer is 17.
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