Skip to lesson

Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

Geometry · Chapter 6 · Lesson 3

Practice Worksheet

Tangents and Chords

A tangent meets the radius at a right angle.

11 problems · about 22 minutes · G-C.A.2, G-C.A.4

NameDate

Figure — use these to answer the problems

A radius, a tangent, and the line to the external point form a right triangle.
adjacent = 5opposite = 12hyp = 13
Radius5
Tangent length12
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Radius 6, tangent 8. Distance to the centre?

    Answer

  2. Radius 5, tangent 12. Distance to the centre?

    Answer

  3. One tangent from a point is 9. The other from the same point?

    Answer

  4. A radius perpendicular to a chord of 10. Each half is?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. How many points does a tangent share with the circle?

    Answer

  2. How many points does a chord share with the circle?

    Answer

  3. Radius 8, distance to centre 17. Tangent length?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Chord 24, bisected by a radius. Half the chord?

    Answer

  2. Match each line to how it meets the circle.

    Draw a line from each item on the left to its match on the right.

    • Tangent
    • Chord
    • Diameter
    • Touches at one point
    • Joins two points on the circle
    • A chord through the centre

  3. The Right Angle

    A tangent meets a radius at what angle, in degrees?

    Answer

  4. To the Centre

    Radius 3, tangent 4. Distance from the external point to the centre?

    Answer