The figure is a circle with centre O and diameter 10 cm. PQ = 1 cm. Then the length of RS is

3 cm

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4 cm

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6 cm

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8 cm

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Solution

The correct option is C
6 cm

Given, diameter = 10 cm

$⟹$ OR = OQ = 5 cm

and, OP = OQ - PQ = 5 cm - 1 cm = 4 cm

Using Pythagoras' theorem in $△$ OPR,

$R P = \sqrt{O R^{2} - O P^{2}} = 3 cm$

We know that the perpendicular from the centre to a chord bisects the chord. Hence RS = 6 cm (as RP = 3 cm)

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The figure is a circle with centre O and diameter 10 cm. PQ = 1 cm. Then the length of RS is

The correct option is C 6 cm Given, diameter = 10 cm ⟹ OR = OQ = 5 cm and, OP = OQ - PQ = 5 cm - 1 cm = 4 cm Using Pythagoras' theorem in △OPR, RP=√OR2−OP2=3 cm We know that the perpendicular from the centre to a chord bisects the chord. Hence RS = 6 cm (as RP = 3 cm)