In a circle with center O. a diameter AB is produced to a…

In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.
John was an artist (1)______ profession. He was very (2)______ at his work and could
(3)______ any subject he could think of, but circumstances forced him to (4)______ in
(5)______ the work of renowned artists.

In a circle with center O. a diameter AB is produced to a point P lying outside the circle and PT is a tangent to the circle at a point C on it, If ∠BPT = 28°, then what is the measure of ∠BCP?

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 31°

PT is a tangent to the circle at point C.

∠BPT = 28^o

In Δ OCP -

∠OCP + ∠COP + ∠OPT = 180^o

90^o + ∠COP + 28^o = 180^o (OC is perpendicular to tangent PT)

∠COP = 180^o - 118^o = 62^o

In Δ OCB -

Let ∠OCB = ∠OBC = x (OC = OB = Radius)

∠OCB + ∠OBC + ∠COB = 180^o

x + x + 62^o = 180^o

2x = 118^o

x = 59^o

∠OCB = ∠OBC = x = 59^o

∠OCP = ∠OCB + ∠BCP

90^o = 59^o + ∠BCP

∠BCP = 90^o - 59^o = 31^o

SSC CGL 2021 PYQ — Question 53