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
In cyclic quadrilateral PQRS, ∠P = (3x + 4)° and ∠R = (2x + 41)°. Find x.
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Question 2
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 26° and ∠BAC = 46°. Find ∠ACD.
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Question 3
ABCD is a cyclic quadrilateral. ∠DAB = 120°. Find ∠BCD.
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Question 4
In cyclic quadrilateral PQRS, ∠P = (3x + 9)° and ∠R = (2x + 91)°. Find x.
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Question 5
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 50° and ∠BAC = 57°. Find ∠ACD.
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Question 6
ABCD is a cyclic quadrilateral. ∠ABC = 74°. Find ∠ADC.
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Question 7
In cyclic quadrilateral PQRS, ∠P = (3x − 6)° and ∠R = (3x + 24)°. Find x.
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Question 8
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 33° and ∠BAC = 70°. Find ∠ACD.
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Question 9
ABCD is a cyclic quadrilateral. ∠ABC = 111°. Find ∠ADC.
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Question 10
In cyclic quadrilateral PQRS, ∠P = (3x + 16)° and ∠R = (3x + 68)°. Find x.
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Question 11
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 44° and ∠BAC = 21°. Find ∠ACD.
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Question 12
ABCD is a cyclic quadrilateral. ∠ABC = 52°. Find ∠ADC.
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Question 13
In cyclic quadrilateral PQRS, ∠P = (3x + 0)° and ∠R = (3x − 48)°. Find x.
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Question 14
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 21° and ∠BAC = 22°. Find ∠ACD.
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Question 15
ABCD is a cyclic quadrilateral. ∠ABC = 111°. Find ∠ADC.
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Question 16
In cyclic quadrilateral PQRS, ∠P = (2x + 11)° and ∠R = (2x + 49)°. Find x.
Answer
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