iGCSE Mathematics (0580) - C4.7 Circle theorems- Exam Style Questions Paper 3- New Syllabus
▶️ Answer/Explanation
(a)
Total interior angle sum $= (8 – 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ$
One interior angle = $\frac{1080^\circ}{8} = 135^\circ$
✅ Answer: $135^\circ$
(b)
The angle between a tangent and a radius (or diameter) is $90^\circ$. So, angle ABE = $90^\circ$ and angle ABD = $90^\circ$.
Since the whole angle from diameter AB to tangent BD is $90^\circ$, and angle ABC is given as $71^\circ$,
$x = 90^\circ – 71^\circ = 19^\circ$
✅ Answer: $x = 19$ because the angle between the tangent and radius is $90^\circ$.
▶️ Answer/Explanation
(a)
Triangle AOB is formed by two radii (OA and OB), making it an isosceles triangle.
✅ Answer: $x = 65$, because base angles of an isosceles triangle are equal.
(b)
AC is a straight line through the origin, which makes it the diameter of the circle.
✅ Answer: Angle in a semicircle equals $90^{\circ}$.
(c)
Because angle ABC is $90^{\circ}$, and angle $ABO = x = 65^{\circ}$, the remaining part of the angle $y$ is just $90^{\circ} – 65^{\circ}$. Alternatively, you can calculate angles in triangle OBC.
✅ Answer: $y = 25$, because angle sum of a triangle equals $180^{\circ}$ (or complementary angles adding to 90).