GCSE Secondary Maths Age 13-17 - Graphs: Circle and Tangent - Explained

The video tutorial explains how to find the area of triangle OAP, where line L is a tangent to a circle at point A, and L crosses the X-axis at point P. The teacher draws a diagram to visualize the problem, identifies the right angle formed by the radius and tangent, and calculates the area using base times height divided by two. The tutorial emphasizes understanding the geometric setup and solving the problem without a calculator, highlighting the importance of planning and applying learned concepts.

What is the equation of the circle given in the problem?

• x^2 + y^2 = 40

• x^2 + y^2 = 20

• x^2 + y^2 = 50

• x^2 + y^2 = 30

What is the center of the circle described in the problem?

• (0, 0)

• (2, 6)

• (1, 1)

• (5, 5)

Why is it important to draw a diagram for this problem?

• To calculate the area directly

• To visualize the triangle and understand the problem better

• To determine the radius of the circle

• To find the exact coordinates of point P

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

• They are parallel

• They do not intersect

• They intersect at a 45-degree angle

• They are perpendicular

What is the gradient of the line OA?

• 2

• 1/2

• -1/3

• 3

What is the equation of the tangent line L?

• y = -1/3x + 20/3

• y = 3x + 2

• y = -3x + 20

• y = 1/3x + 6

What is the x-coordinate of point P where the tangent crosses the x-axis?

• 2

• 6

• 10

• 20

What is the base of triangle OAP?

• 20

• 6

• 10

• 40

What is the height of triangle OAP?

• 10

• 3

• 20

• 6

What is the area of triangle OAP?

• 120 square units

• 60 square units

• 40 square units

• 30 square units