Partly Circles

What is the same and what is different about these circle questions? What connections can you make?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

Partly Circles printable sheet

 

Here are three problems involving circles.

Can you solve them?

Can you find relationships between the three problems?

Firstly Show that ab = cd (where a, b, c, d are lengths)

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Partly Circles

Secondly:

These three circles are drawn so that they touch each other, and their centres are all on the line AB.

If CD is $8$ units in length, what is the area of the region shaded yellow?

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Partly Circles

Lastly: If the area shaded yellow is equal to the area of the larger of the two blue circles, what is the relationship between the radii of the three circles?

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Partly Circles