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A line can touch a circle without crossing it.

What this track covers

Chapter 10 of your Mathematics book is Circles. It is short. A theorem is a fact that is proved. Two theorems are its main ideas.

• The tangent — touches the circle at one point and does not cross.
• The count — a point gives none, one, or two tangents.
• The square corner — at the contact, radius meets tangent at 90°. Proved.
• The length — find a tangent's length with the right angle.
• The equal pair — two tangents from one outside point are equal. Proved.
• The tags — a circle inside a four-sided shape gives equal pieces. We mark them with letters.
• The kite — two tangents decide an angle at the centre.
• One line, two jobs — a chord can touch a smaller circle.

Quick catch-up

Five earlier lessons help here.

• Circle parts — radius, chord, and the centre.
• The centre's line to a chord — at 90°, it halves the chord.
• Naming a triangle's sides — the hypotenuse faces the right angle.
• Finding a shorter side — hypotenuse squared minus one side squared.
• The RHS test — same right angle, hypotenuse and side: a match.

That is the whole track. One touching line, and everything it proves.