Circle theorems
10th grade (Year 11 in England) · 16 questions · Common Core: HSG.C.A.3 · England: GCSE Higher Geometry
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Score/ 16
Question 1
ABCD is a cyclic quadrilateral. ∠ABC = 61°. Find ∠ADC.
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Question 2
In cyclic quadrilateral PQRS, ∠P = (4x + 2)° and ∠R = (2x + 76)°. Find x.
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Question 3
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 54° and ∠BAC = 47°. Find ∠ACD.
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Question 4
ABCD is a cyclic quadrilateral. ∠ABC = 103°. Find ∠ADC.
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Question 5
In cyclic quadrilateral PQRS, ∠P = (3x + 9)° and ∠R = (3x + 33)°. Find x.
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Question 6
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 59° and ∠BAC = 67°. Find ∠ACD.
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Question 7
ABCD is a cyclic quadrilateral. ∠DAB = 57°. Find ∠BCD.
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Question 8
In cyclic quadrilateral PQRS, ∠P = (4x − 3)° and ∠R = (3x + 29)°. Find x.
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Question 9
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 63° and ∠BAC = 69°. Find ∠ACD.
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Question 10
ABCD is a cyclic quadrilateral. ∠ABC = 58°. Find ∠ADC.
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Question 11
In cyclic quadrilateral PQRS, ∠P = (2x + 10)° and ∠R = (x + 62)°. Find x.
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Question 12
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 44° and ∠BAC = 52°. Find ∠ACD.
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Question 13
ABCD is a cyclic quadrilateral. ∠DAB = 60°. Find ∠BCD.
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Question 14
In cyclic quadrilateral PQRS, ∠P = (3x + 4)° and ∠R = (x + 72)°. Find x.
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Question 15
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 32° and ∠BAC = 66°. Find ∠ACD.
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Question 16
ABCD is a cyclic quadrilateral. ∠ABC = 84°. Find ∠ADC.
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