Tangent segments; the inscribed and circumscribed circles of a triangle
- How many tangents through a point — 3 tasks
- The right angle at a point of contact — 3 tasks
- Two tangents from one point — 3 tasks
- Round the inscribed circle — 3 tasks
- Two other ways in — 6 tasks
- Practice — 25 tasks
- Summary — 2 tasks
- Cool-down — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
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How Many Tangent Lines Through a Point? Inscribed and Circumscribed Circles — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each telling where a point P is: by the radius or the diameter and the distance OP, or by a triangle and its inscribed or circumscribed circle. Students sort each piece by the number of tangent lines through P: two, exactly one, or none.
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Tangent Segments Round an Inscribed Circle — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a scalene triangle with its inscribed circle and the points of tangency marked. Students use the equal tangent segments from each corner to find a piece, a perimeter, or a piece on the far side of the triangle. The wrong answers are the two commonest mistakes: pairing the two pieces that meet at a point of tangency, and counting each length once. The row of box numbers at the foot is the check.
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Tangent Segments: Must They Be Equal? — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a triangle with its inscribed circle or a circle with two tangent segments from a point outside it, with two segments drawn thick. Students decide whether the two thick segments must be equal: the two pieces from one corner, yes; the two pieces of one side, no. Fill it or leave it white, and a picture appears.
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Tangent Segments Round an Inscribed Circle — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a scalene triangle with its inscribed circle and the points of tangency marked. Students use the equal tangent segments from each corner to find a piece from the three sides, a perimeter from three pieces, or a piece on the far side of the triangle. Pairing the two pieces that meet at a point of tangency, or counting each length once, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.