Can one help me with this?
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Answer:
Step-by-step explanation:
Since Segment BOA is a diameter:
Arc Ac and Arc CB are in a ratio of two to four. Since Segment BOA is a diameter, Arc ACB measures 180°. Letting the unknown value be <em>x</em>, we can write that:
Hence:
Thus, Arc CB = 120°. By the Inscribed Angle Theorem:
Therefore, ΔABC is a 30-60-90 triangle. Its sides are in the ratios shown in the image below.
Since AC is opposite from the 30° triangle, let AC = <em>a</em>.
We are given that AC = 9. Hence, <em>a</em> = 9.
BC is opposite from the 60° angle and it is given by <em>a</em>√3. Therefore:
