Answers:
a = 63
b = 27
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Step-by-step explanation:
For now, focus on triangle COA.
Since OC and OA are the two radii, this means OC = OA. Furthermore, it means triangle COA is isosceles.
Any isosceles triangle has its base angles congruent to one another. In this case, the base angles are A and C. Both are equal to lowercase 'a'.
So now we know that triangle COA has angles A = a, C = a, O = 54. The three angles of any triangle add to 180
C+O+A = 180
a+54+a = 180
2a+54 = 180
2a = 180-54
2a = 126
a = 126/2
a = 63
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Now turn your attention to triangle ABC. This is a right triangle (due to Thales Theorem). The right angle is at angle C, so C = 90.
Use the same idea as before to find b
A+B+C = 180
a+b+90 = 180
63+b+90 = 180
b+153 = 180
b = 180-153
b = 27