Cogito
Geometry · Chapter 6 · Lesson 3
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
What this lesson teaches
The student applies tangent and chord properties.
- A tangent meets the radius at the point of contact at 90°.
- Two tangents drawn from the same external point are equal.
- A radius perpendicular to a chord bisects it.
Warm Up
Straightforward practice. Get the method working first.
4 problemsRadius 6, tangent 8. Distance to the centre?
Answer 10
Why 10.
Radius 5, tangent 12. Distance to the centre?
Answer 13
Why 25 + 144.
One tangent from a point is 9. The other from the same point?
Answer 9
Why They are equal.
A radius perpendicular to a chord of 10. Each half is?
Answer 5
Why It bisects it.
Build It Up
The same ideas with more to keep track of.
3 problemsHow many points does a tangent share with the circle?
Answer 1
Why It touches.
How many points does a chord share with the circle?
Answer 2
Why Both ends.
Radius 8, distance to centre 17. Tangent length?
Answer 15
Why 289 − 64.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsChord 24, bisected by a radius. Half the chord?
Answer 12
Why Half.
Match each line to how it meets the circle.
Answer Tangent → Touches at one point; Chord → Joins two points on the circle; Diameter → A chord through the centre
Why A diameter is a special kind of chord.
The Right Angle: A tangent meets a radius at what angle, in degrees?
Answer 90
Why 90°.
To the Centre: Radius 3, tangent 4. Distance from the external point to the centre?
Answer 5
Why 5.