Circumference With Letters

Part of the Circles section of Coddy's Geometry journey. Lesson 9 of 62.

When the diameter or radius is an expression, the circumference rule gives an equation. The board writes it with your labels, with both sides already divided by π, so π shows up only as π over π. Cancel it, and the line you solve has no π in it.

$Circle O with diameter x plus 3 and circumference 12 pi$

Here C = 12π and the diameter is x + 3. The rule says 12π = π(x + 3). The board writes it as 12π/π = x + 3, and cancelling π leaves 12 = x + 3, so x = 9. Check it: the diameter is 12, and π × 12 = 12π.

Tap the diameter, pick Circumference, and solve the line the board writes.

Challenge

BA is a diameter of circle O, and the circumference is given. Tap the diameter, pick the rule that connects it to the circumference, and solve the equation the board writes for x.

Then press Check.

Try it yourself

$Use the figure to find x$