Properties of Angles in Circles

The video tutorial explains the properties of inscribed angles in semicircles, highlighting that an inscribed angle in a semicircle is always 90° due to its intercepted arc being 180°. It also covers the properties of chords and tangents, emphasizing that the angle formed by a chord and a tangent is half of its intercepted arc. These concepts are crucial for solving problems involving missing angles in circles.

What is the special property of an angle inscribed in a semicircle?

• It is always 45°.

• It is always 60°.

• It is always 90°.

• It is always 120°.

How can you identify a diameter in a circle?

• It is parallel to the tangent.

• It is perpendicular to the radius.

• It is the longest chord in the circle.

• It passes through the center of the circle.

What is the measure of the intercepted arc in a semicircle?

• 180°

• 90°

• 120°

• 150°

What fraction of the intercepted arc is an inscribed angle?

• One-third

• One-fourth

• One-half

• Equal

If an inscribed angle intercepts a 180° arc, what is the angle's measure?

• 45°

• 60°

• 120°

• 90°

What happens to the inscribed angle if the intercepted arc is increased?

• The angle increases.

• The angle decreases.

• The angle remains the same.

• The angle becomes obtuse.

What is the measure of an inscribed angle if the intercepted arc is 90°?

• 60°

• 45°

• 90°

• 30°

What is a key property of inscribed angles in a semicircle?

• They are always right angles.

• They are always straight angles.

• They are always obtuse.

• They are always acute.

What is the relationship between a diameter and an inscribed angle in a semicircle?

• The diameter is perpendicular to the angle.

• The angle is always 180°.

• The angle is always 90°.

• The diameter bisects the angle.

What is the relationship between a chord and a tangent at the point of contact?

• They are parallel.

• They form a right angle.

• They are equal in length.

• They bisect each other.