Name: Jennifer

Who is asking: Student
Level: Secondary

Question:
two parallel chords of a circle, AB and CD, have lengths of 10 cm and 17 cm respectively. The diameter of the circle is 21 cm. Find the shortest distance between the chords.

Hi Jennifer,

In the diagram OBP is a right angled triangle with |OB| = 21/2 cm, and |BP| = 10/2 cm so |OP|^2 = |OB|^2 - |BP|^2 = 441/4 - 100/4 = 341/4 cm^2. Thus |OP| = Sqrt(341/4) cm. Using the same technique you can find the distance from the center of the circle to the chord BC and then a subtraction gives the distance you want. Cheers, Harley