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4024/11 May/Jun 2023, Question 19: Congruent Triangles: Proof Conditions

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Using the circle with centre O, tangents TA and TB, prove triangles OBT and OAT congruent, justifying each statement.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Solution · 3 marks

  1. 1OA = OB (radii of the same circle)
  2. 2AT = BT (tangents from the same point T are equal)
  3. 3Angle OAT = angle OBT = 90° (tangent is perpendicular to the radius)
  4. 4So triangles OBT and OAT are congruent (SAS)

AnswerOA = OB (equal radii), AT = BT (equal tangents), angle OAT = angle OBT (tangent perpendicular to radius), [congruent] SAS Alternatively: OT is common, angle OAT = angle OBT (tangent perpendicular to radius), OA = OB (equal radii) or AT = BT (equal tangents), [congruent] RHS Alternatively: OT is common, AT = BT (equal tangents), OA = OB (equal radii), [congruent] SSS

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