Circle Theorems and Properties

This video tutorial covers various circle theorems, including the properties of chords, tangents, subtended angles, and cyclic quadrilaterals. It explains how angles in semicircles are always 90 degrees and how angles subtended by the same arc are equal. The video also discusses the relationship between tangents and chords and provides a problem-solving example to illustrate these concepts. Viewers are encouraged to engage with the content and ask questions if needed.

What is a chord in a circle?

• A line that passes through the center of the circle

• A line that forms a right angle with the radius

• A line that lies anywhere below the diameter

• A line that touches the circle at one point

Tags

CCSS.HSG.C.A.2

What is the angle formed by a triangle inside a semicircle?

• 90°

• 45°

• 60°

• 120°

Tags

CCSS.HSG.C.A.2

What is the angle between a tangent and the radius at the point of contact?

• 120°

• 90°

• 60°

• 45°

What is a subtended angle?

• An angle formed by two radii

• An angle formed by an arc opposite to the inner triangle

• An angle formed by two tangents

• An angle formed by a chord and a tangent

What is true about angles in the same segment subtended by the same arc?

• They are always 45°

• They are always 60°

• They are always equal

• They are always 90°

Tags

CCSS.HSG.C.A.2

What is the relationship between the inner angle of an arrowhead shape and the angle at the circumference?

• The inner angle is equal to the angle at the circumference

• The inner angle is twice the angle at the circumference

• The inner angle is half the angle at the circumference

• The inner angle is three times the angle at the circumference

What is unique about the opposite angles in a cyclic quadrilateral?

• They add up to 90°

• They add up to 360°

• They are always equal

• They add up to 180°

Tags

CCSS.HSG.C.A.2

What is true about the lengths of two tangents drawn from an external point to a circle?

• They are always equal

• They are always different

• One is twice the length of the other

• One is half the length of the other

Tags

CCSS.HSG.C.A.2

What is the alternate segment theorem?

• The angle between two chords is equal to the angle in the alternate segment

• The angle between a radius and a chord is equal to the angle in the alternate segment

• The angle between two tangents is equal to the angle in the alternate segment

• The angle between a tangent and a chord is equal to the angle in the alternate segment

Tags

CCSS.7.G.B.5

In the example problem, what is the final angle marked D?

• 55°

• 70°

• 90°

• 35°

Tags

CCSS.7.G.B.5