SSC CGL 17 Aug 2021 Shift 3 Paper

Question : 53 of 100

Marks: +1, -0

Points

A

and

B

are on a circle with centre O. PAM and

P B N

are tangents to the circle at

A

and

B

respectively from a point

P

outside the circle. Point

Q

is on the major arc

A B

such that,

∠ Q A M=58^{∘}

and

∠ Q B N=50^{∘}

, then find the measure (in degrees) of

∠ A P B

Solution:

Given,

∠ Q A M=58^{∘}

and

\;\; ∠ Q B N=50^{∘}

△ Q O A, Q O=O A=

radius
Then,

∠ O Q A=∠ O A Q=x^{∘}

△ O Q B, Q O=O B=

radius
Then,

∠ O Q B=∠ O B Q=y^{∘}

Now,

∠ M A P=∠ M A Q+∠ Q A O+∠ O A P

[linear angle]

⇒ 58^{∘}+x+90^{∘}=180^{∘} ⇒ x=32^{∘}

Now,

∠ N B P=∠ N B Q+∠ Q B O+∠ O B P

[linear angle]

⇒ 50^{∘}+y+90^{∘}=180^{∘} ⇒ y=40^{∘}

Now,

∠ B Q A=∠ B Q O+∠ O Q A

=32^{∘}+40^{∘}=72^{∘}

Then,

∠ B O A=2 × ∠ B Q A

[ ∵

Angle made on centre is double of angle made at circumference]

=2 × 72^{∘}=144^{∘}

Now, In

\square O B A P

∠ O+∠ A+∠ P+∠ B=360^{∘}

⇒ ∠ A P B=360^{∘}-144^{∘}-90^{∘}-90^{∘}=36^{∘}

Go to Question:

Prev Question

Next Question