Tangent Segment Theorem

ATB is a tangent to each circle with centre O. Find the size of each angle.

• x = 34°

  y = 11°

  z = 15°

• x = 65°

  y = 69°

  z = 46°

• x = 46°

  y = 69°

  z = 65°

In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x

• 38

• 52

• 90

• 72

In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x

• 70

• 110

• 140

• 90

Identify which circle theorems you could use to solve each question

• Angle between tangent and radius is 90°

• Angle is in semicircle is 90°

• Opposite angles of cyclic quadrilateral add to 180°

• Angle is same segment are equal

• Two angles in isoceles triangle the same

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

Find the length of the missing segment.

• 12

• 34

• 169

• 13

Identify which circle theorems you could use to solve each question

• Angle between tangent and radius is 90°

• Angle is in semicircle is 90°

• Opposite angles of cyclic quadrilateral add to 180°

• Angle is same segment are equal

• Angles of quadrilateral add to 360°

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

Name the tangent line. 

• s

• WR

• VT

• QR

Lines AO and BO are tangent. What is the measure of BO?

• 20

• 15

• 10

• 5