# The length of the circle chord is 60, and the distance from the center of the circle to this chord is 40. Find the diameter of the circle

May 31, 2020 | Education

| Denote the key points as shown. Draw a segment of AO.

Consider the triangle AOB.

This triangle is right-angled, since the distance OB is the height (shortest distance).

AB is equal to half the length of the chord (according to the third property of the chord).

Then, by the Pythagorean theorem:

AO ^ 2 = OB ^ 2 + AB ^ 2

AO ^ 2 = 40 ^ 2 + (60/2) ^ 2

AO ^ 2 = 1600 + 900 = 2500

AO = 50 is the radius of the circle, therefore, the diameter D = 2 * AO = 100

Answer: D = 100

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