Let O be the centre of a circle. PA and PB are tangents to…

Comprehension:
In the following passage, some words have been deleted. Select the most appropriate option
to fill in each blank.
In the 19th century, there was an industrial revolution in Europe. As a result, millions of people
left the (1) ______ and went to work in big factories in cities. Today, it is the reverse. In several
major cities, people have started moving out. Why? They want a cleaner, (2) ______
environment. There are fewer jobs in ‘heavy’ industries like steel and power generation. (3)
______, there are more jobs in service industries like banking, tourism and food delivery.
Besides, modern transport and communications have made it easier for people to (4) ______
to work or even work from home. The result of this revolution in the 21st century will be
‘spread cities’ – cities are growing fast, but (5) ______, away from city centres and people are
choosing to live 40, 50 or 60 kilometres away.

Let O be the centre of a circle. PA and PB are tangents to the circle from a point P outside the circle and A and B are points on the circle. If angle APB = 50º, then angle OAB is equal to:

Show answer & explanation

Correct answer: A

Explanation

The correct answer in option 1 i.e. 25º

In quadrilateral OAPB, ∠O + ∠A + ∠P + ∠B = 360°

⇒ ∠O + 90° + 50° + 90° = 360°

⇒ ∠O = 360° - 230° = 130°

In ΔOAB, OA = OB = radius

⇒ ∠O + ∠B + ∠A = 180° ( By the property of angle sum )

⇒ 130° + ∠B + ∠A = 180° ( ∠OAB = ∠OBA )

⇒ ∠A + ∠B = 180° - 130° = 50°

(∵ Angles opposite to equal sides are equal.)

⇒ ∠A + ∠A = 50°

⇒ ∠A = 50°/2 = 25°

SSC CHSL 2021 PYQ — Question 54