CIRCLE GEOMETRY

Multiple Choice

A tangent of a circle is ...

• a line that has endpoints on the circle and passes through the centre of the circle.

• a straight line that touches the circle at a single point.

• a region of the circle bounded by two radii and an arc lying between the radii.

• a line joining the centre of the circle to any point on the circumference circle.

Multiple Choice

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Solve for "?" (the length of the hypotenuse)

• 15

• 6

• -24

• 14

Multiple Choice

What can be concluded about the lengths of the tangents AP and BP drawn from point P to the circle?

• AP is longer than BP

• AP is shorter than BP

• AP is equal to BP

• AP and BP cannot be compared

Multiple Choice

What are the two segments created by a chord in a circle?

• Major and Minor Segments

• Upper and Lower Segments

• Left and Right Segments

• Inner and Outer Segments

Multiple Choice

What does the perpendicular line from the center of a circle to a chord do?

• It bisects the chord

• It extends beyond the chord

• It creates a right angle

• It forms a triangle

Multiple Choice

If two chords AB and CD are the same length then they will be the same perpendicular distance from the centre of the circle. What can be concluded about the distances OP and OQ?

• OP > OQ

• OP < OQ

• OP = OQ

• OP + OQ = AB

Multiple Choice

Find the value of x.

• 30°

• 48°

• 60°

• 75°

Multiple Choice

Find the value of x in the given circle diagram where the angle at the circumference is 62°.

• 76°

• 124°

• 180°

• 90°

Multiple Choice

Which angle property do we use in the diagram?

• angle at the centre = 2 angles at the circumference

• common angles

• angle subtended by different arcs

• angle in the same segment

Multiple Choice

Find the value of x in the given circle diagram where the angle at the circumference is 104°.

• 104°

• 75°

• 105°

• 360°

Multiple Choice

Find m∠ EGF. EF is a diameter of the circle.

• 45°

• 60°

• 90°

• 100°

Multiple Choice

What is the value of x and y?

• x=75°; y=93°

• x=65°;y=104°

• x=75°; y=94°

• x=65°; y=93

Multiple Choice

What is the size of angle x?

• 19^o
• 76^o
• 39^o
• 38^o

Fill in the Blank

The chords EH and FG of the circle are produced to meet at X. Given that $$\angle EGH\ =\ 40\degree$$  and XH = HF = FE, calculate $$\angle HXG$$  

Fill in the Blank

TV is a diameter of the circle. Given that UW = UV and $$\angle VUW\ =\ 30\degree$$  , calculate $$\angle UVT$$  

Fill in the Blank

In the circle, the diameter QS intersects the chord PR at M, the midpoint of PR. Given that O is the centre of the circle and $$\angle POQ\ =\ 136\degree$$  , calculate $$\angle RSQ$$  

Fill in the Blank

In the figure, PT is a tangent to the circle, centre O and POS is a diameter. The radius OR is parallel to PT, the line TO cuts the circle at Q and $$\angle OTP\ =\ 36\degree$$  

Find $$\angle QSR$$  

Poll

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