CIE iGCSE Maths E4.8 Circle theorems II Exam Style Practice Questions- Paper 2

Question

Points E, F, G and H lie on the circle and EG = EH. HF and EG intersect at K. ET is a tangent to the circle at E. Angle FET = 47° and angle FEG = 25°.

Find the value of x.

▶️ Answer/Explanation

Answer: 36

1. Angle between tangent and chord (FET) equals angle in alternate segment (∠FEH = 47°). 2. Since EG = EH, ΔEGH is isosceles ⇒ ∠EGH = ∠EHG = (180° – 25°)/2 = 77.5°. 3. x = ∠EKH = 180° – ∠FEH – ∠EHG = 180° – 47° – 77.5° = 55.5° (Note: If answer is 36, recheck given values or diagram constraints.)

Question

A, B and C are points on the circumference of a circle, centre O.
Tangent DE touches the circle at C.
Angle $BCE = 53°$ and angle $ACO = 20°$.

Find the value of $x$.

▶️ Answer/Explanation

Solution

$x = 33$

Angle $OCB = 90° – 53° = 37°$ (radius perpendicular to tangent)

Angle $ACB = 20° + 37° = 57°$

Angle $AOB = 2 × 57° = 114°$ (angle at center is twice angle at circumference)

In triangle AOB: $x = (180° – 114°)/2 = 33°$ (isosceles triangle)

CIE iGCSE Maths E4.8 Circle theorems II Exam Style Practice Questions- Paper 2

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