# In the figure, if ∠BAC = 80° then find the value of ∠BCP.

AC is the diameter

ACP = 90° [radius is perpendicular to tangent]

ABC = 90° [angle in a semicircle is 90°]

ABC + BAC + ACB = 180° [sum of internal angles in a triangle is 180°]

ACB + 90° + 80° = 180°

ACB = 180 – 170

ACB = 10°

BCP = ACP - ACB

= 90 – 10

= 80°

BCP = 80°

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