Worksheet: Circle Theorem
Calculator Paper
Show all working of the following questions
1. In the diagram A, B, C, and D lie on the circle, centre O. EA is a tangent to the circle
at A. Angle EAB = 61° and angle BAC = 55°.
61°
64°
128°
29° 26°
116°
64°
a. Find angle BAO
29°
…………………………………………………………………………………… [1]
b. Find angle AOC
128°
………………………………………………………………………………….... [2]
c. Find angle ABC
64°
…………………………………………………………………………………… [1]
d. Find angle CDA
116°
…………………………………………………………………………………… [1]
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2. A, B, C and D are points on the circumference of the circle, centre O. DOB is a
straight line and angle DAC = 58°.
90°
58°
32°
Find angle CDB.
32°
…………………………………………………………………………………… [3]
3. P, Q, and R are points on the circumference of the circle, centre O. PO is parallel to
QR and angle POQ = 48°.
48°
Find angle OPR.
24°
……………………………………………………………………………………. [2]
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4. A, B, C, D and E lie on the circle, centre O. Angle AEB = 35°, angle OED = 28° and
angle ACD = 109°.
62°
62°
8°
36°
71° 28°
124°
35°
8° 47°
118°
Work out the following angles, giving reasons for your answers.
124/2 = 62, it is half the angle at the
62°
a. Angle EBD = ………………………………
because ……………….………
[3]
centre point
it equals to EBD, angles coming from the
62°
b. Angle EAD = ………………………………
because ……………….………
same chord are equal [2]
5. K, L, and M are points on the circle. KS is a tangent to circle at K. KM is a diameter
and triangle KLM is isosceles.
90°
45°
90°
45°
90° 90°
Find the value of z.
z= 45° because 90 - 45= 45
……………………………………………………………………………………. [2]
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6. F, G, H and J are points on the circle. EFG is a straight line parallel to JH.
72°
108°
72°
108°
y= 72°
……………………………………………………………………………………. [2]
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Worksheet: Circle Theorem
Non Calculator Paper
Show all working of the following questions
1. Points A, B, C, D, E, and F lie on the circle, centre O.
Find the value of x and find the value of y.
55°
𝑥 = ……………………………… [1]
𝑦 = ……………………………… [1]
24°
2. A, B and C are points on the circle, centre O.
Find the obtuse angle AOC.
130 x 2 = 260°
360 - 260 = 100°
……………………………………………………………………………………. [2]
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3. The diagram shows a circle, centre O. AB and DE are chords of the circle. M is the
midpoint of AB and N is the midpoint of DE.
AB = DE = 9 cm and OM = 5 cm.
9cm
9cm
Find ON.
5cm
……………………………………………………………………………………. [1]
4. The points A, B, C, D and E lie on the circumference of the circle. Angle DCE = 47°
and the angle CEA = 85°.
85°
95°
FInd the values of
95°
𝑤 = ……………………………… [1]
𝑥 = ……………………………… [1]
48°
[1]
𝑦 = …………….…………………
85°
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5. A, D, C, and D are points on the circumference of the circle. AX and BD intersect at
X.
Complete the statement
equal
Triangle ADX is …………………………
to triangle BCX [1]
6. A, B, C, and D lie on the circle, centre O. Angle ABC = 131°.
29°
Find angle ADC.
49°
……………………………………………………………………………………. [1]
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