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CAIE IGCSE Mathematics Extended E4.8.1 Use the Following Symmetry Properties of Circles Equal Chords Are Questions

Practise Extended CAIE IGCSE Mathematics by applying equal-chord, arc and angle symmetry relationships in circles.

Syllabus
2028–2030
Course
Mathematics 0580
Level
Extended

Exam points

  • Use equal chords and equal angles in a circle to solve geometry problems.
  • Interpret perpendicular bisectors, arcs and central or inscribed angles from circle symmetry.
  • Apply circle symmetry properties to justify lengths or angle relationships.

CAIE IGCSE Mathematics Extended E4.8.1 Use the Following Symmetry Properties of Circles Equal Chords Are Questions question 1

[Maximum number: 5]
Figure for Question CAIE IGCSE Mathematics Extended E4.8.1 Use the Following Symmetry Properties of Circles Equal Chords Are Questions question 1 — CAIE IGCSE Mathematics Extended

NOT TO SCALE
P and Q are points on the circle with centre O.
TP and TQ are tangents to the circle from the point T.
Complete the following statements and reasons.
In triangles OPT and OQT
O P= ...... because each is a radius of the circle
OT is a common side

Angle O P T= angle ...... =90^ because ......
Triangles OPT and OQT are congruent using the criterion ......
This proves that the tangents TP and TQ are ......

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