Question

Question:33 PA is the tangent to the circle with centre O while PC
bisects the angle APB. What is the measure of angle ACP?
(a)30°
(b)45°
(c)60°
(d) 75°​

Answer 1

Given :  PA is the tangent to the circle with centre O while PC bisects the angle APB

To find : measure of angle ACP

Solution:

lets join AO

AO = BO   = radius

=> ∠OAB  =∠OBA  = x

∠OAP = 90°   as PA is Tangent

∠BAP = x + 90°

∠BAP + ∠ABP + ∠APB = 180°

=> x + 90° + x + ∠APB = 180°

=> ∠APB = 90° - 2x

∠APC  = (1/2)  ∠APB

=> ∠APC  = (1/2)  (90° - 2x)

=> ∠APC  = 45° - x

in ΔACP

∠CAP + ∠APC + ∠ACP = 180°

∠CAP = ∠BAP

=>  x + 90° + 45° - x  + ∠ACP = 180°

=> ∠ACP = 45°

measure of angle ACP = 45°

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Answer 2

Answer:

The answer is 45. here is ur solution