Equal radii: find the missing length
A circle has two radii drawn from its centre to its edge, with a point partway along each, and the two inner parts are the same length. The student types one length: a leftover piece from a point to the edge, an inner part, the radius or the diameter, or both leftover pieces added together. Many questions show a plain circle; others are a flower bed with paths and lamps, a bicycle wheel with spokes and beads, a pizza with cuts and olives, a pond with ropes and floats, or a field with chalk lines and cones.
The key is that both lines run from the centre to the edge, so both are radii and the same length. Take the same inner part off each, and the leftover pieces must be equal too. The radius is not always given plainly: it may come as the diameter, to halve, or as the length of the other radius, named by its letters. Sometimes the inner parts are only said to be equal, with no number. The working lights up both radii on the picture, writes in each length as it is found and marks the two leftover pieces equal. The usual slip is using the diameter as if it were the radius.
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What changes each time
- Four kinds: a leftover piece, an inner part, the radius or diameter, or both leftover pieces added together
- The radius given plainly, as the diameter, or as the other radius by its letters; the equal inner parts given as numbers or only said to be equal
- Radii from 6 to 40 cm on a plain circle, 10 to 36 cm for pizzas and wheels and 6 to 40 m outdoors; a quarter of the questions use one decimal place
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- Faces, edges and vertices (Grade 3)
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- Turning and flipping letters (Grade 3)
- Counting squares of every size (Grade 3)
- Inside or outside the loop (Grade 3)
- Which piece fills the gap? (Grade 3)
- Symmetry on a grid (Grade 4)
- Rotations and reflections (Grade 4)
- Reading a protractor (Grade 4)
- Parallel and perpendicular lines (Grade 4)
- Parts of a circle (Grade 4)
- Draw without lifting your pencil (Grade 4)
- Can these sticks make a triangle? (Grade 4)
- Lines, rays and line segments (Grade 4)
- Counting line segments (Grade 4)
- Triangle from two circles (Grade 4)
- Splitting an angle in half (Grade 4)
- 3D shapes: side view (Grade 5)
- Rectangle in a quarter circle (Grade 5)
- Painted cube puzzle (Grade 5)
- Rope around the Earth (Grade 5)
- Can dominoes cover the board? (Grade 5)
- Most crossing points of straight lines (Grade 5)
- Angles in a circle (Grade 6)
- Congruent triangles: match the corners first (Grade 6)
- Vertically opposite angles (Grade 6)
- Inscribed circle in a right triangle (Grade 8)
- SSS and SAS: is it enough to prove congruence? (Grade 8)