Circle Theorems: 12 Theorems Based on Circles

The video tutorial covers theorems related to circles, focusing on equal chords, their converse, and angles subtended by arcs. The teacher explains how to prove these theorems using properties of triangles and congruency. The session includes a recap of previous theorems and introduces new ones, emphasizing the importance of understanding the relationships between angles, chords, and arcs in a circle.

What is the main concept used to prove that equal chords are equidistant from the center of a circle?

• Properties of triangles

• Properties of squares

• Properties of rectangles

• Properties of hexagons

In the converse of theorem six, what must be proven to show that equidistant chords are equal?

• The triangles formed are congruent

• The chords are parallel

• The chords are tangent

• The chords are perpendicular

According to the theorem, how does the angle subtended by an arc at the center compare to the angle subtended at any point on the circle?

• It is half the angle

• It is double the angle

• It is equal to the angle

• It is triple the angle

Which theorem is used to prove that the angle subtended by an arc at the center is double the angle subtended at any point on the circle?

• Exterior angle theorem

• Interior angle theorem

• Pythagorean theorem

• Alternate angle theorem

What is the relationship between angles in the same segment of a circle?

• They are complementary

• They are supplementary

• They are equal

• They are different

What special case is discussed in the theorem about angles in the same segment?

• When the segment is a semicircle

• When the segment is a quarter circle

• When the segment is a full circle

• When the segment is a triangle

What is the angle subtended in a semicircle according to the special case discussed?

• 45 degrees

• 180 degrees

• 60 degrees

• 90 degrees