A point P moves such that it is equidistant from Points Q and R. Find QR when PR = 8cm and angle PRQ = 30°

  • A 4√3cm
  • B 8cm
  • C 8√3cm
  • D 4cm
jamb 2001mathematics

The correct answer is C. 8√3cm

PQ (r)  = PR (q) = 8cm

R° = Q° = 30°

Sum of angles in a triangle = 180°

P° + Q° + R° = 180°

P° + 30° + 30° = 180°

P° = 180° - 60°

p° = 120°.

PQ = r, PR = q, QR = p 

Using sine rule:

\(\frac{p}{sinP}\) = \(\frac{q}{sinq}\)

\(\frac{p}{sin120°}\) = \(\frac{8}{sin30°}\)

cross multiply

p = \(\frac{8 X sin120°}{sin30°}\)

p = \(\frac{8 X √3/2 }{1/2}\)

p = 8√3

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