JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Circle

The diameter of the circle, whose centre lies on the lines

x + y = 2

in the first quadrant and which touches both the lines

x = 3

and

y = 2

, is ______.

Answer: 3

Solution

With the centre on

x + y = 2

in the first quadrant, write it as

(α, 2 - α)

. Touching both

x = 3

and

y = 2

means its distances to these lines are equal and each equals the radius:

∣3 - α ∣ = ∣2 - (2 - α) ∣ = ∣ α ∣

. For

0 < α < 2

this gives

3 - α = α

, so

α = \frac{3}{2}

and the radius is

\frac{3}{2}

. The diameter is therefore

3

Structure Geometric configuration — Geometric configuration

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Integer answer

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