GCSE Maths | Circle Theorems
- The angle between a tangent and radius is always 90o
- The angle at the centre is always double the angle at the circumference
- The angle formed by a semi circle is always 900.
- Opposite angles in a cyclic quadrilateral add up to 180o.
- Two angles from the same points are equal.
- Angles in the alternate segment are equal.
Question 1
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a) $x = 25^\circ$
b) $x = 56^\circ$
c) $x = 18^\circ$
Question 2
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a) $x = 102^\circ$
b) $x = 61^\circ$
c) $x = 70^\circ$
Question 3
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a) $x = 50^\circ$
b) $x = 24^\circ$
c) $a = 37^\circ$, $b = 37^\circ$
Question 4
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a) $x = 83^\circ$, $y = 104^\circ$
b) $x = 130^\circ$, $y = 95^\circ$
c) $x = 109^\circ$, $y = 140^\circ$
Question 5
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a) $x = 63^\circ$
b) $x = 22^\circ$
Question 6
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a) $x = 70^\circ$
b) $x = 55^\circ$, $y = 60^\circ$
c) $x = 65^\circ$, $y = 63^\circ$, $z = 52^\circ$
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