Geometric reasoning and proof

The points A, B and C lie on the circumference of a circle.

The straight line DCE is a tangent to the circle. AB = BC. ACB = x, where x is measured in degrees.

Find an expression for the size of ACD. Give your answer in terms of x.

You must give a reason for each step of your solution.

P, Q and R are points on the circumference of a circle with centre O.

Calculate the value of x. You must state all the angle properties that you use.

You must show all your working.

P, Q and R are points on the circumference of a circle with centre O.

Calculate the value of x. You must state all the angle properties that you use.

You must show all your working.

Is it possible for an isosceles triangle to have an angle of 140°? Circle your answer.

You must give an explanation for your answer.

YES NO

Which of the following equations is correct for the diagram shown above?

Circle your answer.

a + b = 30 a + b = 210 b – a = 150

a – b = 150 a + b = 150

Is it possible for an isosceles triangle to have an angle of 140°? Circle your answer.

You must give an explanation for your answer.

YES NO

Is it possible for a rhombus to have an angle of 120° and an angle of 30°? Circle your answer.

You must give an explanation for your answer.

YES NO

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A regular octagon with centre O is shown below.

Calculate the exact size of OAB. You may choose to draw additional lines on the diagram to help you.

You must show all your working.

A, B and C are points on the circumference of a circle with centre O.

ACB = 74°.

Calculate the value of x. You must state any angle property of a circle that you use.

You must show all your working.

ABCD is a quadrilateral.

Calculate the value of x.

When ABCD is drawn to scale, would the lines AD and BC be parallel or not?

You must justify your answer without using a scale drawing.

ABCD is a quadrilateral.

Calculate the value of x.

When ABCD is drawn to scale, would the lines AD and BC be parallel or not?

You must justify your answer without using a scale drawing.