Circle Geometry and Chord Properties

The video tutorial covers the geometry of circles, focusing on the perpendicular bisector of a chord. It explains how a perpendicular from the center of a circle to a chord bisects the chord. Through examples, it demonstrates calculating lengths using this property and applying the Pythagorean theorem to solve problems involving right triangles formed within circles. The tutorial includes practice questions to reinforce understanding and concludes with a summary of key concepts.

What is a chord in a circle?

• A line that passes through the center of the circle.

• A line that touches the circle at only one point.

• A line segment with both endpoints on the circle.

• A line that is tangent to the circle.

According to the perpendicular bisector theorem, what happens when a radius is drawn to a chord?

• The chord is divided into three equal parts.

• The chord is bisected at right angles.

• The radius becomes the diameter.

• The chord is extended beyond the circle.

In Example 1, if AC is 12 cm, what is the length of BC?

• 12 cm

• 18 cm

• 6 cm

• 24 cm

In Example 2, if the whole line AB is 36 mm, what is the length of BC?

• 24 mm

• 9 mm

• 36 mm

• 18 mm

In Example 3, what is the length of CO if the radius is 10 cm and AB is 16 cm?

• 10 cm

• 8 cm

• 12 cm

• 6 cm

What theorem is used to solve for the missing side in a right triangle formed by a chord and radius?

• Cosine rule

• Sine rule

• Pythagorean theorem

• Thales' theorem

In Practice Question 1, if OM is perpendicular to AB and AM is 9 cm, what is the length of BM?

• 18 cm

• 9 cm

• 12 cm

• 6 cm

In Practice Question 2, if AB is 42 cm and the hypotenuse is 29 cm, what is the length of OM?

• 20 cm

• 21 cm

• 29 cm

• 25 cm

In Practice Question 3, if AM equals BM and the angle at the center is 42 degrees, what is the value of angle X?

• 180 degrees

• 90 degrees

• 42 degrees

• 138 degrees

In Practice Question 4, if the radius is 7.5 cm and the other side is 4 cm, what is the length of X?

• 6.34 cm

• 8 cm

• 7 cm

• 5 cm