Circles (Edexcel A-Level Mathematics): Flashcards

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Angle in a Semicircle
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What is Thales' Theorem about angles in a circle?

Any angle subtended by the diameter is a right angle.

What shape does Thales' Theorem involve?

A triangle inscribed in a circle with one side as a diameter.

What is the key angle in Thales' Theorem?

Angle ACB is a right angle (9090 degrees).

What is the first step in proving Thales' Theorem?

Draw the circle and the inscribed triangle.

What does Thales' Theorem state about angles in a circle?

The angle in a semicircle is a right angle.

What does Thales' Theorem state about angles in a semicircle?

Angles subtended by a diameter are right angles.

What is used to relate angles in the circle?

Angles OCA and OCB subtend the same arc AB.

What represents angles on a straight line in proof?

AOC+ABC=180AOC + ABC = 180 degrees.

What is a practical use of Thales' Theorem?

To solve problems involving circles and right triangles.

What verifies a triangle as a right triangle using Thales?

Check if AC2+BC2=AB2AC^2 + BC^2 = AB^2.

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