2 Answers

In the diagram POQ is a diameter of the circle PQRS….

Posted by: 209 views
MATHS

QuizTablet Community!
In the diagram POQ is a diameter of the circle PQRS.... » QuizTablet

In the diagram POQ is a diameter of the circle PQRS. If <PSR = 145°. Find x

  • A. 45°
  • B. 25°
  • C. 35°
  • D. 55°

QUICK ANSWER…

D

SOLUTION 

If one of the sides of a triangle is the diameter of a circle, and the three angles of the triangle intersect with the circumference of the circle, then the angle opposite the diameter is always 90°, that is a rule in circle geometry. It is demonstrated below:

in the diagram POQ is a diameter of the circle PQRS. If

If PQ is the diameter, then <PSQ must be = 90° irrespective of where S touches the circumference.

If <PSQ = 90°, then <RSQ = 145 – 90 = 55°

Now there’s another rule in circle geometry, it states that if the chord of a circle makes two or more angles at any point on the circumference, these angles are absolutely the same.

For instance, in the diagram above, there are 4 chords: PQ, PS, SR, and RQ.

For chord PQ: angle PRQ and angle PSQ form a base with chord PQ, this rule states that <PRQ = <PSQ.

RELATED!  From the diagram above, find the value of OTQ

Similarly, for chord PS, angle PRS = angle PQS

For chord SR, angle SPR = angle SQR

And for chord RQ, angle RPQ = angle RSQ

Therefore since <RPQ = x° which is also same as <RSQ. hence, x = 55°

Now for the right answer to the above question:

  1. Option A is incorrect.
  2. Option B is incorrect.
  3. C is incorrect.
  4. D is the correct answer.

QUICK TIPS…

You may please note these/this:

  • Always remember that when two angles form between the same chord and different points on the same side of the circumference of a circle, they are definitely the same.
  • A chord is any straight line joining two points on the circumference of a circle.

Use the questions and answers session to deal further on this topic…

You can also freely share this page with friends.

/ culled from 2018 JAMB-UTME mathematics question 4 /

In the diagram POQ is a diameter of the circle PQRS.... » QuizTablet
In the diagram POQ is a diameter of the circle PQRS.... » QuizTablet

ORIGINALLY ANSWERED!!!

Course Provider: Organization

Course Provider Name: N.D Sammy

Course Provider URL: QuizTablet.com

Editor's Rating:
8.1

Answer Question