Case study·Standard multi-step (3/5)·No calculator

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

A circular roundabout has centre OO and radius 77 m. A straight road from point PP just touches the roundabout at TT. The distance OPOP is 2525 m.
Total: 4 marks

(a) State the angle between OTOT and the road PTPT. (1 mark)

(b) Find PTPT. (2 marks)

(c) If another tangent from PP touches the roundabout at SS, find PSPS. (1 mark)

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