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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( Plane Geometry MathRoom Index )

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