Question

The diameter of the circle is 34cm and a chord is at a distance of 15cm from the centre. Find the length of the chord of the circle

Answer 1

Answer:  16 cm

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Explanation:

The drawing is shown below.

• Point A = center of circle
• Points B,C,E = points on the circle's edge
• Point D = midpoint of chord CE

The goal is to find the length of CE based on these facts

• BC = 34 = diameter
• AD = 15 = distance from center to chord
• x = length of segment CD = length of segment DE

Notice how AB = AC = AE = 17 because they are all radii of the same circle. We cut the diameter in half to get the radius.

Focus on triangle CAD. We'll use the pythagorean theorem to find x.

a^2 + b^2 = c^2

(AD)^2 + (DC)^2 = (AC)^2

15^2 + x^2 = 17^2

225 + x^2 = 289

x^2 = 289 - 225

x^2 = 64

x = sqrt(64)

x = 8

Segment CD is 8 cm long, and so is segment DE.

To wrap things up, we then say:

CE = CD + DE

CE = 8 + 8

CE = 16

Chord CE is 16 cm long.