Tangent lines and the radius
- Three lines, three counts — 3 tasks
- The perpendicular is the shortest — 3 tasks
- The right angle at the point of contact — 3 tasks
- Which segment to draw — 3 tasks
- Going Deeper — 6 tasks
- Practice — 23 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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Tangent Lines and the Radius: Is the Line Tangent? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 circles drawn to scale, each with a line. Students decide from the marks and the numbers, not the look of the line: tangent (a right angle with the radius, three sides with the right angle at the point of tangency, or the distance equal to the radius), not tangent, or cannot tell. Two pieces look tangent and their numbers say no.
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Tangent Lines and the Radius: The Right Angle at the Point of Tangency — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a circle drawn to scale with a line through a point of it and no right angle marked. Students use the right angle between a tangent and the radius to find a radius, a diameter or an angle, and decide once whether a line is tangent from three lengths. The wrong answers are the two commonest mistakes: giving the diameter for the radius, and losing the right angle at the point of tangency. The row of box numbers at the foot is the check.
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Tangent Lines and the Radius: Where Is the Right Angle? — Mystery Picture 25–35 minutes · 5 sheets
25 circles, each with a line tangent at T and one angle marked with a small arc. Students compute nothing: a tangent is perpendicular to the radius at the point of tangency, so is the marked angle that right angle, or an angle at P, at the center, at another point of the line, or beside a chord? Fill it or leave it white, and a picture appears.
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Tangent Lines and the Radius: The Right Angle at the Point of Tangency — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a circle drawn to scale with a line tangent to it at T and no right angle marked. Students draw the radius to the point of tangency, use the right angle there, and find a radius, a diameter or an angle, always a whole number. Giving the diameter for the radius, or forgetting the right angle, lands on a card that sends the group back. A clean run is 8 lines on the record sheet.