Geometric Proof (AQA GCSE Further Maths): Exam Questions

and are points on the circumference of a circle.

Work out the size of angle .

.......................degrees

and are points on the circumference of a circle, centre .

is a tangent to the circle at . Angle Angle Angle

Work out the value of .

............................degrees

and  are points on a circle.

Prove that  is a diameter.

and are points on a circle, centre .

is a straight line. Angle

Prove that   .

, and are points on a circle, centre .

The line is a diameter of the circle.

The line is parallel to the line .

Angle

The line is shown.

Work out the size of angle in terms of .

and are points on a circle.

Chords and intersect at . is a tangent to the circle. and are parallel.

Angle = 2

Give reasons why angle and angle are also equal to 2.

Angle ......................................

Angle ...................................

Work out the values ofand .

You must show your working. Do not use trial and improvement.

  and are points on a circle.

and are points on a different circle, centre .

and are straight lines.

angle

Prove that angle .

In the case when is parallel to , work out the size of angle .

...........................degrees

, , and are points on a circle.

is a tangent.

The straight line is parallel to .

Prove that is parallel to .

Use angle as  to help you.