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

2 \sqrt{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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

Suggest Corrections

Similar questions

Q. Recall that two circles are congruent if they have the same radius then equal chords of congruent circles subtend equal angles at their centres.

Q. If the circles of same radius

a

and centres at

(2, 3)

and

(5, 6)

cut orthogonally, then

a

is equal to

State true or false

Two congruent circles with centres O and O' intersect at two points A and B Then

∠ A O B = ∠ A O^{'} B

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Q. Recall that two circles are congruent, if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres

Join BYJU'S Learning Program

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