Question

Let right angled isosceles triangle ABC be inscribed in a circle according to adjacent diagram vertex A is moved along the circle to reach at A' such that are \[{\stackrel\frown{AA'}}\] = `(πr)/3`, if r = `sqrt(3) + 1` then (A'C)² is ______.

पर्याय

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

Let right angled isosceles triangle ABC be inscribed in a circle according to adjacent diagram vertex A is moved along the circle to reach at A' such that are AA' = `(πr)/3`, if r = `sqrt(3) + 1` then (A'C)² is 2.00.

Explanation:

∵ ∠AOA' = 60°

∴ ∠ABA' = 30°

⇒ ∠A'BC = 45° – 30° = 15°  ...(∵ ∠ABC = 45°)

Now in right angle triangle A’ BC

sin15° = `("A"^'"C")/(2r)`

⇒ A'C = `2.(sqrt(3) + 1). (sqrt(3) - 1)/(2sqrt(2)) = sqrt(2)`

⇒ (A'C)² = 2