Let a triangle A B C be inscribed in the circle x 2 - 2 x + y + y 2 = 0 such that ∠ B A C = π 2 .…

Let a triangle ABC be inscribed in the circle x2-2x+y+y2=0 such that ∠BAC=π2. If the length of side AB is 2, then the area of the △ABC is equal to:
  1. 1
  2. 6+32
  3. 3+32
  4. 6+234

Solution

Given,

circle x2-2x+y+y2=0

With centre 12,12 and radius 1.

Since ∠BAC=π2, so BC will act as diameter,

BC=diameter=2  (given)

So, AC=BC2-AB2=2 and AB=2

Now, △ABC=12AB·AC=1  

Asked in: JEE Main 2022 (29 Jun Shift 2)

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