**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:**

**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.**

**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:**

**Option A is incorrect.****Option B is incorrect.****C is incorrect.****D is the correct answer.**

**QUICK TIPS…**

**You may please note the****se/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…**

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**/**** ****culled from ****201****8 ****JAMB-UTME ****mathematics ****question**** 4 ****/**