GeminiHeat wrote:
Attachment:
Arcs.gif
The length of arc AXB is twice the length of arc BZC, and the length of arc AYC is three times the length of arc AXB. What is the measure of angle BCA?
A. 20
B. 40
C. 60
D. 80
E. 120
Let \(O\) be the centre of the circle
\(AXB + BZC + CYA = 2πr\)
\(2(BZC) + BZC + 3(2BZC) = 2πr\)
\(9BZC = 2πr\)
\(BZC = \frac{2}{9}πr\)
Let the angle subtended by \(BZC\) be \(x\)
\(BZC = \frac{x}{360}(2πr)\)
Therefore, \(\frac{x}{360}(2πr) = \frac{2}{9}πr\)
\(x = 40\)
i.e. \(∠BOC = 40\), \(∠BOA = 80\), and \(∠AOC = 240\)
Using Central Angle property:\(∠BCA = \frac{1}{2}∠BOA\)
\(∠BCA = \frac{1}{2}(80) = 40\)
Hence, option B