Geometric Proof (AQA GCSE Further Maths)

A, B and C are points on a circle, centre O.

Work out the size of angle .

 ............................... degrees[5]

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 ...................................

[2]

Work out the values ofand .

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

[4]

and are points on a circle, centre .

is a straight line.
Angle

Prove that   

[5]

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[4]

  and are points on a circle.

and are points on a different circle, centre .

and are straight lines.

angle

Prove that angle

[3]

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

...........................degrees[2]

Points A, B and C lie on a circle, centre O.

Angle AOC = 
Angle ABC = 

Work out the value of .

........................... degrees[3]

D, E, F and S are points on a circle.

RST is a tangent.

The straight line EDT is parallel to FS.

DS = DT

Prove that FD is parallel to RST.

Use angle DTS as  to help you.

[5]

A, B, C and D are points on a circle, centre O.

Which statement is correct?

Tick one box.

[1]

and are points on a circle, centre.

Work out the value of

[3]

x = ......................degrees

is parallel to .

Prove that   

[4]

and are points on the circumference of a circle.

w: y = 7 : 5

Work out the size of angle .

[4]

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