CIRCLE GEOMETRY QUESTIONS

Using the theorems you learned on circle geometry, do these questions.

Here's a link to the solutions (right click the link, choose "open in a new window")

1/ TC is tangent, AB = OB, angle TCA = 50°. Show that angle CAB = 100°

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2/ AD is a diameter, angle BAD = 30 ⁰, angle CDA = 28 ⁰,

The degree measure of arc CB is:

a) 128º

b) 64º

c) 58º

d) 122º

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3/ AP = BP, TP is tangent, angle APT = x°

The measure of angle OBA is:

a) (45 – ½ x)º

b) xº

c) (2x – 90)º

d) (90 – x)º

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4/ The measure of angle ACB is:

a) 30°

b) 40°

c) 60°

d) 20°

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5/ PT is tangent at T and PT = 12 cm. PB : BA = 4 : 5.

The length of PA is:

a) 2 cm.

b) 9 cm.

c) 18 cm.

d) 36 cm.

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6/ Find the length of the radius r.

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7/ PA and PB are tangents. angle P = 72°:

angle ACB is:

a) 54°

b) 108°

c) 57°

d) 36°

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8/ AB = 13 cm., EB = 4 cm., CE = ED:

The length of CD is:

a) 36 cm.

b) 6 cm.

c) 12 cm

d) not given

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9/ AB is the diameter of a circle center O. Through A, draw a straight line
which cuts the circle again at C and meets the tangent at B in point D.
Prove that AC:AB = AB:AD.

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10/ Circle center O is divided into two unequal segments by chord MN.
L is any point on the minor arc MLN.
Prove that angle MLN is 90° greater than angle OMN.

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