The big picture
Here is the track, one idea per line.
| Idea | Remember | Example |
|---|---|---|
| The tangent | Touches at one point, does not cross | A drawn wheel meets the road once |
| The count | Distance vs radius: less none, equal one, more two | 3, 5, 7 against radius 5 give 0, 1, 2 |
| The square corner | Radius ⊥ tangent at the contact point — proved | Every rim point, every tangent |
| The length | tangent² = distance² − radius² | 13 and 5 give tangent 12 |
| The equal pair | Two tangents from one outside point are equal — proved. | TP = TQ |
| The tagging | Equal tangent pieces at each vertex of a quadrilateral round a circle | AB + CD = BC + DA |
| The kite | Junction angle plus centre angle add to 180° | 70° and 110° |
| More facts | OT cuts angle POQ in half. Tangents at a diameter's ends are parallel. | Angle PTQ 64°: angle POT 58° |
| One line, two jobs | A chord of one circle can touch a smaller, same-centre circle | Half-chord² = outer radius² − inner radius² |
Chapter 10 of your Mathematics book is Circles. You now know the two proofs of this chapter. You also know the right triangle, and three places the theorems apply.
Next: Areas Related to Circles — sectors and segments of the same circles.