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:
AO2 = OB2 + AB2
AO ^ 2 = 27 ^ 2 + (72/2) ^ 2
AO ^ 2 = 729 + 1296 = 2025
AO = 45 is the radius of the circle, therefore, the diameter D = 2 * AO = 2 * 45 = 90
Answer: D = 90
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