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JAMB Mathematics 1992 Question 26

Question 26

Circle Theorems

In the fig. above, PQR is a semicircle while PQ and QR are chords. QS is the perpendicular from Q to the diameter PR. What is the expression for QS?

Diagram for this question
  1. A.QS = PS.SR
  2. B.QS = √(PS.SR)
  3. C.QS = √2 √(PS.SR)
  4. D.QS = (1/√2) √(PS.SR)
Show the answer and explanation

Answer: B (QS = √(PS.SR))

Explanation

Angle PQR is 90° (angle in a semicircle), so triangles PSQ and QSR are similar. This gives QS/PS = SR/QS, i.e. QS2 = PS × SR.