The radius of the circles which pass through the point ( 2 , 3 ) and cut off equal chords of length 6 units along the lines y − x − 1 = 0 and y + x − 5 = 0 is ' r ' then [ r ] is (where [.]

Question

The radius of the circles which pass through the point ( 2 , 3 ) and cut off equal chords of length 6 units along the lines y − x − 1 = 0 and y + x − 5 = 0 is ' r ' then [ r ] is (where [.] denotes greatest integer function)

TestHub · Accepted Answer

The given two lines pass through the point $(2, 3)$ and are inclined at $4 5^{\circ}$ and $13 5^{\circ}$ to the x axis the other ends of chords can easily be calculated as

$(2 + 32, 3 + 32) and (2 - 32, 3 - 32)$

There is symmetry about the line $x = 2$ and therefore the centres of circles lie on $x = 2$ As the chords subtend right angles at the centre.

$∴ 2 r^{2} = 6^{2} \Rightarrow r = 32$

Mathematics - Circle Question with Solution | TestHub

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