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Answer:
∠ BCD = 30°
Step-by-step explanation:
The tangent- secant angle CBD is half the difference of its intercepted arcs.
arc CD = 360° - (96 + 162)° = 360° - 258° = 102° , then
∠ BCD = ( AC - CD) = (162 - 102)° = 0.5 × 60° = 30°
We are asked to solve for the angle AOB and we are given with the following values:
radius = 12 cm
length of AB = 15 cm
We can solve for angle AOC such as shown below:
sin AOC = opposite/hypotenuse
sin AOC = 7.5/12
∠AOC =38.68°
The angle subtended at the center of the circle is just twice of ∠AOC, then we have:
∠AOB = 38.68° x 2
∠AOB = 77.36°
The answer is 77° 21' 51.75".