In a circle with centre O, AOC is the diameter. B is a point on the circumference of the circle such that are AB is $\frac{1}{5}$
In a circle with centre O, AOC is the diameter. B is a point on the circumference of the circle such that are AB is $\frac{1}{5}$ of the arc BC. What is the degree measure of ∠BOC?
एक वृत्त जिसका केंद्र O है, उसमें AOC एक व्यास है। बिंदु B वृत्त की परिधि पर स्थित है, तथा चाप AB, चाप BC का $\frac{1}{5}$ है। $\angle BOC$ का मान (डिग्री में) ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
150°
Since AC is a diameter, the arc AC = $180^\circ$.
Let the arc $AB = x^\circ$.
Then arc $BC = 5x^\circ$.
So,
$x+5x=180^\circ$
$6x=180^\circ$
$x=30^\circ$
Hence,
Arc $BC = 150^\circ$.
The central angle $\angle BOC$ is equal to the measure of arc $BC$.
$\therefore \angle BOC = 150^\circ$.
Answer: $150^\circ$
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