Segment relationships: power of a point
- Four chords, one number — 3 tasks
- The crossed triangles — 3 tasks
- Near times far — 6 tasks
- When the two points become one — 3 tasks
- The number that belongs to the point — 3 tasks
- Practice — 24 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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Power of a Point: Correct, Wrong, or Cannot Tell? Segment Lengths in Circles — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 drawings of chords, secants and tangents, each with an equation. Students do not solve: they sort each equation as correct, wrong (the wrong pieces, or the tangent not multiplied by itself), or cannot tell, because the two lines do not meet at one point or a line misses the circle.
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Power of a Point: Chords, Secants and Tangents — Segment Lengths in Circles Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a circle with two chords, two secants, or a tangent and a secant, drawn to scale with a number on every piece. Students find x, a whole number. The wrong answers are the two commonest mistakes: multiplying the wrong two pieces, and forgetting the square root for a tangent. The row of box numbers at the foot is the check.
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Power of a Point: Secants and Tangents — Segment Lengths in Circles Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a circle with two secants or a tangent and a secant from one outside point, drawn to scale with a number on every piece and an equation such as 4 × (4+5) = 3 × (3+x). Students solve nothing: they decide whether the equation uses the right pieces. Fill it or leave it white, and a picture appears.
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Power of a Point: Chords, Secants and Tangents — Segment Lengths in Circles Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a circle with two chords, two secants, or a tangent and a secant, drawn to scale with a number on every piece. Students find x with the same rule inside and outside the circle: near times far on one line equals near times far on the other. Multiplying the wrong pieces or forgetting the square root lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.