Circle Theorems and Properties

This video tutorial covers various circle theorems, including angles in the same segment, angles in a semicircle, the relationship between angles at the center and circumference, cyclic quadrilaterals, tangents and radii, and the alternate segment theorem. It also demonstrates how to apply these theorems to solve geometry problems.

What is the name of the line that goes from one side of the circle to the other?

• Tangent

• Chord

• Diameter

• Radius

According to the first circle theorem, what can be said about angles in the same segment?

• They are supplementary

• They are complementary

• They are equal

• They are right angles

What is the angle in a semicircle?

• 60 degrees

• 90 degrees

• 45 degrees

• 120 degrees

If the angle at the circumference is 50 degrees, what is the angle at the center using the same chord?

• 75 degrees

• 100 degrees

• 50 degrees

• 25 degrees

What is a cyclic quadrilateral?

• A quadrilateral where all vertices lie on the circumference of a circle

• A quadrilateral with one pair of parallel sides

• A quadrilateral with all angles equal

• A quadrilateral with all sides equal

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

• 45 degrees

• 60 degrees

• 120 degrees

• 90 degrees

What can be said about tangents drawn from the same external point to a circle?

• They are perpendicular

• They are equal in length

• They are parallel

• They are unequal in length

What does the alternate segment theorem state?

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

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

• Opposite angles in a cyclic quadrilateral add up to 180 degrees

• Angles in the same segment are equal

In a cyclic quadrilateral, if one angle is 110 degrees, what is the measure of the opposite angle?

• 80 degrees

• 70 degrees

• 90 degrees

• 100 degrees

If a triangle is inscribed in a circle and one of its sides is the diameter, what is the measure of the angle opposite to this side?

• 60 degrees

• 45 degrees

• 90 degrees

• 120 degrees