P,Q,R,S,T are points on a circle with centre O so that ∠PTQ= 2 x ∠RTS and PQ

Question

P,Q,R,S,T are points on a circle with centre O so that $∠$ PTQ= 2 x $∠$ RTS and PQ %undefined RS. Find $∠$ SOQ, if P,O,Q are in a straight line

Options:

A . 45

^{\circ}

B . 90

^{\circ}

C . 60

^{\circ}

D . 30

^{\circ}

Answer: Option A
:
A

$∠$ PTQ= 90 (angle in a semi circle)

, hence $∠$ RTS = 45.

$∠$ ROS = 90 ( Inscribed angle= 2 *Angle at circumference)

OR=OS=OR (radius)

$∠$ RSO = $∠$ SOQ= 45 $^{\circ}$ (interior alternate angles)

Option (a)

Was this answer helpful ?

Next Question

More Questions on This Topic :

Question 1. In an equilateral triangle ΔABC, D divides BC in the ratio 2 : 1 while E divides AC in the ratio 1 : 2. Find BE : ED ?....the ratio 1 : 2. Find BE : ED ?

Question 2. In a triangle ABC, M is the mid-point of BC. If ∠AMB = 45∘, and ∠ACM = 30∘, then ∠B....∠ACM = 30∘, then ∠BAM is (∠B is not obtuse)

Question 3. What is the minimum area of quadrilateral ABCD, if the area of a pair of diagonally opposite triangles (Formed by join....the diagonals of the quadrilateral) is 12 and 27 respectively?

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0