Generalizations and Related Results
Thales' theorem is a special case of the following theorem:
- Given three points A, B and C on a circle with center O, the angle AOC is twice as large as the angle ABC.
See inscribed angle, the proof of this theorem is quite similar to the proof of Thales' theorem given above.
A related result to Thales' theorem is the following:
- If AC is a diameter of a circle, then:
-
- If B is inside the circle, then ∠ABC > 90°
- If B is on the circle, then ∠ABC = 90°
- If B is outside the circle, then ∠ABC < 90°.
Read more about this topic: Thales' Theorem
Famous quotes containing the words related and/or results:
“In the middle years of childhood, it is more important to keep alive and glowing the interest in finding out and to support this interest with skills and techniques related to the process of finding out than to specify any particular piece of subject matter as inviolate.”
—Dorothy H. Cohen (20th century)
““The ideal reasoner,” he remarked, “would, when he had once been shown a single fact in all its bearings, deduce from it not only all the chain of events which led up to it but also all the results which would follow from it.””
—Sir Arthur Conan Doyle (1859–1930)