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Circle Theorems: Quiz 8 – Answers
Circle Theorems: Quiz 8 – Answers
1) Proves that angle CAB is equal to angle ABC by using the following steps:
- Uses opposite angels in the cyclic quadrilateral AORC add up to 180° to show that angle ORC is 180° – CAO (or 180° – CAB)
- Uses angles on the straight line CRB add up to 180° to show that angle ORB is the same size as angle CAO (or CAB)
- States that triangles OBR is an isosceles triangle because OR and OB are radii and therefore the same length. This means that angle OBR is the same size as CAO (or CAB) because angle OBR and angle ORB will be equal
- Final statement saying that angle CAB is equal to angle ABC
The content in the section before this quiz goes through the steps in more detail – click here to be taken to the content. Therefore, there is no working for this quiz!
A, B, R and P are four points on a circle with centre O.
A, O, R and C are four points on a different circle.
The two circles intersect at the points A and R.
CPA, AOB and BRC are straight lines.
Prove that:
A, O, R and C are four points on a different circle.
The two circles intersect at the points A and R.
CPA, AOB and BRC are straight lines.
Prove that:
angle CAB = angle ABC.