NIMCET 2025 Paper

Section: Mathematics

Question : 24 of 120

Marks: +1, -0

A circle with its centre in the first quadrant touches both the coordinate axes and the line

x-y-2=0

Then the area of the circle is:

Solution:

If a circle touches both axes in the first quadrant, its centre is at

(r, r)

and radius is

r

.
Distance from centre

(r, r)

to the line

x-y-2=0

must equal the radius

r

\;{|r-r-2|}/{{√{1^2+(-1)^2}}}=r

\;{|-2|}/{{√{2}}}=r

\;{2}/{{√{2}}}=r ⇒ r={√{2}}

Area of the circle:

π r^2=π({√{2}})^2=2 π .

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