Properties of Circles and Angles

The video tutorial covers the properties of circles, emphasizing their importance in DSE exams. It introduces basic circle terminology such as radius, chord, and arc, and explains key circle theorems, including angle properties and cyclic quadrilateral properties. The tutorial also discusses tangent properties and their applications. The instructor provides strategies for remembering these concepts and highlights the significance of understanding rather than memorizing for exam success.

Why is it important to understand the Properties of Circle topic for DSE exams?

• It is not important at all.

• It is related to all other topics.

• It can be understood independently of other topics.

• It is the only topic in the exam.

What is the term used for a line segment joining the center of a circle to any point on the circle?

• Arc

• Diameter

• Radius

• Chord

What happens when a line from the center of a circle is perpendicular to a chord?

• It bisects the chord.

• It forms an arc.

• It creates a tangent.

• It becomes a radius.

If two chords in a circle are equal, what can be said about their distance from the center?

• One is closer to the center.

• They are equidistant from the center.

• They are at different distances.

• They are perpendicular to each other.

What is the relationship between the angle at the center and the angle at the circumference of a circle?

• The angle at the center is half the angle at the circumference.

• The angle at the center is twice the angle at the circumference.

• The angles are equal.

• The angle at the center is thrice the angle at the circumference.

What is the angle formed in a semi-circle?

• 45 degrees

• 60 degrees

• 90 degrees

• 180 degrees

In a cyclic quadrilateral, what is the sum of the opposite angles?

• 360 degrees

• 90 degrees

• 180 degrees

• 270 degrees

What is the property of a tangent to a circle at the point of contact?

• It is parallel to the radius.

• It forms an angle of 45 degrees with the radius.

• It is perpendicular to the radius.

• It bisects the radius.

What is the angle in the alternate segment theorem?

• The angle between the tangent and the chord is equal to the angle at the circumference.

• The angle between the tangent and the chord is equal to the angle at the center.

• The angle between the tangent and the chord is equal to the angle in the same segment.

• The angle between the tangent and the chord is equal to the angle in the opposite segment.

If two tangents are drawn to a circle from an external point, what can be said about the lengths of the tangents?

• They are equal.

• One is longer than the other.

• They are perpendicular.

• They are unequal.