Question
Download Solution PDFComprehension
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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
⇒ 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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