Circles Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
A chord of a circle is 2424 cm long and is 55 cm from the centre. Find the radius of the circle.

Solution

  1. 1
    A perpendicular from the centre to the chord bisects the chord, creating a right triangle with half-chord =12= 12 cm and distance =5= 5 cm.
  2. 2
    Apply the Pythagorean theorem: r2=122+52=144+25=169r^2 = 12^2 + 5^2 = 144 + 25 = 169.
  3. 3
    Take the square root: r=13r = 13 cm.

Answer

r=13ย cmr = 13 \text{ cm}
The perpendicular from the centre to a chord always bisects the chord. This property creates a right triangle where the radius is the hypotenuse, linking circle geometry to the Pythagorean theorem.

About Circles

The set of all points in a plane at a fixed distance (the radius) from a central point called the center.

Learn more about Circles โ†’

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