Exploring Circle Theorems and Their Applications

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 equal to the angle at the circumference.

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

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

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

What is the measure of an angle formed at the circumference by a diameter of a circle?

• 90 degrees

• 180 degrees

• 45 degrees

• 60 degrees

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

• None of the above

• 180 degrees

• 90 degrees

• 45 degrees

What is the angle in a semicircle?

• 45 degrees

• None of the above

• 90 degrees

• 180 degrees

What is true about the angles in the same segment of a circle?

• They are none of the above.

• They are supplementary.

• They are equal.

• They are complementary.

In a cyclic quadrilateral, what is the relationship between opposite angles?

• They are none of the above.

• They are complementary.

• They are supplementary.

• They are equal.

What is the relationship between the base angles of an isosceles triangle formed by two radii of a circle?

• They are complementary.

• They are supplementary.

• They are equal.

• They are none of the above.

What is the property of tangents drawn from a single external point to a circle?

• They are perpendicular to the radius.

• They intersect at the center.

• They are equal in length.

• They are parallel to each other.

What theorem is used to determine the angle between a chord and a tangent?

• Cyclic quadrilateral theorem

• Tangent radius theorem

• Alternate segment theorem

• Segment angle theorem

How do the lengths of two tangents from the same external point to a circle compare?

• They are unequal.

• They are of the same length.

• Cannot be determined.

• One is twice as long as the other.