Circle theorems
10th grade (Year 11 in England) · 16 questions · Common Core: HSG.C.A.2 · England: GCSE Higher Geometry
Name
Date
Score/ 16
Question 1
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 44°, and ∠ABC = 34°. Find ∠BAC.
Answer
Question 2
A tangent touches a circle at A. Chord AB makes an angle of 66° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
Answer
Question 3
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 57°, and ∠ABC = 71°. Find ∠BAC.
Answer
Question 4
A tangent touches a circle at A. Chord AB makes an angle of 26° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
Answer
Question 5
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 55°, and ∠ABC = 50°. Find ∠BAC.
Answer
Question 6
A tangent touches a circle at A. Chord AB makes an angle of 60° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
Answer
Question 7
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 42°, and ∠ABC = 52°. Find ∠BAC.
Answer
Question 8
A tangent touches a circle at A. Chord AB makes an angle of 45° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
Answer
Question 9
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 31°, and ∠ABC = 44°. Find ∠BAC.
Answer
Question 10
A tangent touches a circle at A. Chord AB makes an angle of 27° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
Answer
Question 11
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 61°, and ∠ABC = 45°. Find ∠BAC.
Answer
Question 12
A tangent touches a circle at A. Chord AB makes an angle of 28° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
Answer
Question 13
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 33°, and ∠ABC = 75°. Find ∠BAC.
Answer
Question 14
A tangent touches a circle at A. Chord AB makes an angle of 42° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
Answer
Question 15
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 32°, and ∠ABC = 34°. Find ∠BAC.
Answer
Question 16
A tangent touches a circle at A. Chord AB makes an angle of 29° with the tangent. C is a point on the circle in the other segment. Find ∠ACB.
Answer
Write your answers right on the page. · Free from eurekami.com