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In the cyclic quadrilateral above find PRO

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In the cyclic quadrilateral above find PRO

In the cyclic quadrilateral above find PRO

  • A. 20°
  • B. 30°
  • C. 50°
  • D. 70°

QUICK ANSWER…

A

SOLUTION 

<POR = 110°

We are going to be using two rules in circle geometry,

Rule 1, sum of opposite angles in a cyclic quadrilateral = 180.

Rule 2, angles on a common chord is absolutely the same.

Therefore, applying rule 1,

<POR + <PQR = 180

<PQR = 180 – <POR

<PQR = 180 – 110 = 70°

Hence,

<PQO = 70 – 50 = 20°

Applying rule 2 on chord PO,

RELATED!  In the diagram POQ is a diameter of the circle PQRS....

<PQO = <PRO = 20°

Now for the right answer to the above question:

  1. Option A is correct.
  2. Option B is incorrect.
  3. C is incorrect.
  4. D is not the correct answer. 

KEY-POINTS…

You may please note these/this:

  • Angles on a common chord are the same.
  • A chord is any straight line that touches two points on a circle.

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/ culled from 2016 JAMB-UTME mathematics past question 44 /

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