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4024/21 May/Jun 2021, Question 8: Similar Triangles

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

Circle with centre O through P, Q, R: angle POQ = 8x°, angle RPO = x°, angle OQR = 24°. Find angle PQO. Then similar triangles KLM and KNJ with KL = 6 cm, KM = 10.5 cm, KN = 10 cm and area of JKN = 75 cm²; find y.

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Part (a) · 4 marks

Using the circle with centre O and points P, Q, R, work out the size of angle PQO in degrees.

  1. 1Angle PRQ = 8x ÷ 2 = 4x (angle at centre = 2 × angle at circumference)
  2. 2OP = OR = OQ, so angle ORP = x and angle ORQ = 24°
  3. 3x + 24 = 4x → x = 8
  4. 4Angle POQ = 64°
  5. 5Angle PQO = (180 − 64) ÷ 2 = 58°

Answer58°

Part (b) · 5 marks

Given the similar triangles and the stated lengths and area, determine the value of angle y.

  1. 1Similar triangles: KL/KN = KM/KJ → 6/10 = 10.5/JK
  2. 2JK = 17.5 cm
  3. 3Angle JKN = y (vertically opposite)
  4. 41/2 × 10 × 17.5 × sin y = 75 → sin y = 75/87.5
  5. 5y = 58.99…° ≈ 59.0°

Answer58.99… to 59.0

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Also searched as: 4024/21/M/J/21 · 4024_s21_qp_21 · 4024 s21 21 · question 8.
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