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All 75 Exam Topics Step-by-Step Lesson
Practice 15-Q Timed Drill
Step-by-Step Lesson • Step 1 of 6

ARCH-M1-09: Circle Theorems, Tangent-Radius Right Angles & Shaded Sector Mensuration (Degrees)

Full 15-Q Timed Drill
Step 1 of 6 • The Core Idea

ARCH-M1-09: Why the 150s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~150s (Blows 90s Clock)
The area of the 90∘90^\circ sector OABOAB is 90∘360∘π(62)=9π cm2\frac{90^\circ}{360^\circ}\pi(6^2) = 9\pi\text{ cm}^2. The area of the right-angled isosceles triangle OABOAB is 12×6×6=18 cm2\frac{1}{2} \times 6 \times 6 = 18\text{ cm}^2. Subtracting gives the minor segment area 9π−18 cm29\pi - 18\text{ cm}^2 (~95s).
The Fast ShortcutTarget: 45s (Saves 105s)
**Line 1 (Sector π\pi Term):** 14π(62)=9π\frac{1}{4}\pi(6^2) = 9\pi.
Line 2 (Subtract Right Triangle): 9π−12(6)(6)=9π−189\pi - \frac{1}{2}(6)(6) = 9\pi - 18 (20s).
Where Students Lose Time: In 16 past UAT-UK questions (7.11% of Mathematics 1), candidates lose 105s by halving instead of doubling the subtended angle, or substituting d into pi*r². Instead, apply M5 with Maths 1 skill M5.6.
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