Track quiz
Keep the table beside you. The right angle at the contact point unlocks most of these questions.
| Idea | How it goes |
|---|---|
| The tangent | Touches at one point, does not cross. |
| The count | Distance vs radius: less none, equal one, more two. |
| The square corner | Radius ⊥ tangent at the contact point — proved. |
| The length | tangent² = distance² − radius². |
| The equal pair | Two tangents from one outside point are equal — proved. |
| The tagging | Equal tangent pieces at each vertex of a quadrilateral round a circle. |
| The kite | Junction angle plus centre angle add to 180°. |
| One line, two jobs | A chord of one circle can touch a smaller, same-centre circle. |
In this chapter, what is a tangent?
Three points sit 3, 5 and 7 cm from a centre. The radius is 5 cm. How many tangents through each?
A tangent touches a circle at T. Q is another point on that same tangent line. Where does Q lie?
P is 10 cm from a centre of radius 6 cm. Find the tangent length from P.
P is 13 cm from a centre. A tangent from P is 12 cm long. What is the radius?
Two tangents from P touch a circle at A and B. PA is 9 cm. What is PB?
A circle touches all four sides of ABCD. AB = 8, BC = 6, CD = 10. Find DA.
Two tangents from P meet at 100°. Find the angle between the radii at the centre.
Concentric circles have radii 29 cm and 21 cm. Find the chord of the larger circle that touches the smaller one.
Chapter 10 of your Mathematics book is Circles. You have proved both of its theorems yourself.
Next: Areas Related to Circles — sectors and segments of the same circles.