Learn: Circles: radius, diameter, and touching circles
Strand
Geometry & Visualization GEO
Tier
CoreThe working middle of the exam.
Appears in
5–6 · 7–8 · 9–103 levels
What it is
A circle is every point the same distance from the centre, so the radius is the fact everything else is built on. When circles touch, the distance between their centres is the sum of the radii - drawing that line is usually the move.
●●○4 points, difficulty 2 of 34 ptLevel 5–6about 60s
Two circles touch on the outside. One has a radius of 3 cm and the other a radius of 5 cm. How many centimetres apart are their centres?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Draw the line joining the two centres.
2The strategy
Draw a straight line from one centre to the other. It passes through the point where the circles touch, so it is made of one radius from each circle, laid end to end.
3The full solution
The line from centre to centre is 3 + 5 = 8 cm.
Solution— no shortcut on this one
Draw the line joining the two centres. Because the circles touch on the outside, that line passes through the single point where they meet, so it is exactly one radius of the first circle plus one radius of the second: 3 + 5 = 8 cm. If instead one circle sat inside the other and touched, the distance would be the difference, 5 - 3 = 2 - which is choice A. The transferable idea: joining the centres turns a circle question into a length question.
Why this is on the test: Touching on the outside and touching on the inside give the sum and the difference of the radii, and the two are constantly confused.
Where it goes wrong
Each of these is written the way a student would say it to themselves.
“I used the radius where the problem gave me the diameter.”
“I forgot to draw the line joining the two centres.”
“I assumed a circle inside a square touches the corners rather than the sides.”
Every problem in this skill
●○○3 points, difficulty 1 of 33 ptOne step from a skill you know.
Nothing at this tier yet for GEO-07.
●●○4 points, difficulty 2 of 34 ptTwo steps, or one step plus a trap.