Two chords PQ and RS intersect at point O inside the circle. If OP = 4 cm, OQ = 9 cm and RS = 12 cm, then the value of OR is .

5 cm

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6 cm

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7 cm

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8 cm

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Solution

The correct option is B 6 cm
When two chords intersect each other within a circle, the product of the chord segments will be equal.
So, $O P \times O Q = O R \times O S$
Let the value of OR be 'x' cm
4 $\times$ 9 = x $\times$ (12 - x)
$36 = 12 x - x^{2}$
$x^{2} - 12 x + 36 = 0$
$(x - 6)^{2} = 0$
x = 6 cm

Hence, the value of OR is 6 cm.

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Two chords PQ and RS intersect at point O inside the circle. If OP = 4 cm, OQ = 9 cm and RS = 12 cm, then the value of OR is .

The correct option is B 6 cmWhen two chords intersect each other within a circle, the product of the chord segments will be equal. So, OP×OQ=OR×OS Let the value of OR be 'x' cm 4 × 9 = x × (12 - x) 36=12x−x2 x2−12x+36=0 (x−6)2=0 x = 6 cm Hence, the value of OR is 6 cm.