Comprehension

Direction: Consider the following for the items that follow:

A triangle ABC is inscribed in the circle x2 + y2 = 100. B and C have coordinates (6, 8) and (-8, 6) respectively.

What is BAC equal to?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. π/2
  2. π/3 or 2π/3
  3. π/4 or 3π/4
  4. π/6 or 5π/6

Answer (Detailed Solution Below)

Option 3 : π/4 or 3π/4
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NDA 01/2025: English Subject Test
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Detailed Solution

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Explanation:

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⇒ BC = \(√{(6+8)^2+ (8-6)^2} =√200 = 10√2\)

Let O is centre of circle

x2 +y2 = 100,

Radius = OB = OC = 10 units

OB2 + OC2 = \(√{100+100} = 10√2\)

 In ∆BOC, OB2 + OC2 = BC2 = (10√2 )2

= 200

So ∠ BOC = 90° (by converse of Pythagoras theorem)

Then, ∠ BAC = 45° or 180° – 45° = \(\frac{\pi}{4} or \frac{3\pi}{4}\) .. ((Angle subtended by a chord at centre is double the angle at any point subtended by it on the remaining circle.)

∴ Option (c) is correct.

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