Two congruent circles with centres at $(2, 3)$ and $(5, 6),$ which intersect at right angles, have radius equal to

2 \sqrt{2}

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3

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4

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None of these

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Solution

The correct option is B $3$
It is given that circles intersect each other at $90^{\circ}$
As circles are congruent, they have equal radius.
Hence, $r_{1} = r_{2} = r$

$C_{1} C_{2} = \sqrt{(5 - 2)^{2} + (6 - 3)^{2}}$
$C_{1} C_{2} = \sqrt{18}$

By Pythagoras theorem,
$r^{2} + r^{2} = (C_{1} C_{2})^{2} \Rightarrow 2 r^{2} = (\sqrt{18})^{2}$
$\Rightarrow r^{2} = 9 \Rightarrow r = 3$

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Two congruent circles with centres at (2,3) and (5,6), which intersect at right angles, have radius equal to

The correct option is B 3It is given that circles intersect each other at 90∘ As circles are congruent, they have equal radius. Hence, r1=r2=r C1C2=√(5−2)2+(6−3)2 C1C2=√18 By Pythagoras theorem, r2+r2=(C1C2)2⇒2r2=(√18)2 ⇒r2=9⇒r=3

Two congruent circles with centres at $(2, 3)$ and $(5, 6),$ which intersect at right angles, have radius equal to