Circle Geometry: Circles with Tangents and Inscribed Angles

The video tutorial explains how to solve a geometry problem involving a circle with center O, tangents, and angles. It covers calculating angle AOC using properties of tangents and radii, and then finding angle ADC using circle theorems. The tutorial emphasizes understanding the relationship between angles at the center and circumference, and provides a step-by-step solution with a focus on key points and marks allocation.

What is the given angle ABC in the problem?

• 90 degrees

• 53 degrees

• 74 degrees

• 106 degrees

Why are angles BAO and BCO considered right angles?

• Because they are formed by a tangent and a radius

• Because they are angles in a triangle

• Because they are angles in a quadrilateral

• Because they are opposite angles

How do you calculate angle AOC in the quadrilateral?

• By doubling the angle at the circumference

• By adding all angles in the quadrilateral

• By subtracting the right angles and angle ABC from 360 degrees

• By dividing the angle at the circumference by two

What is the relationship between angle AOC and angle ADC?

• Angle AOC is equal to angle ADC

• Angle AOC is twice angle ADC

• Angle AOC is three times angle ADC

• Angle AOC is half of angle ADC

What is the calculated size of angle ADC?

• 74 degrees

• 106 degrees

• 53 degrees

• 90 degrees

What was the first mark awarded for in the solution?

• Identifying the right angles

• Calculating angle AOC

• Calculating angle ADC

• Understanding the circle theorem

What is the key circle theorem used in this problem?

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

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

• The angle at the center is equal to the angle at the circumference

• The angle at the center is three times the angle at the circumference