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° .

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. .

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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