Maths/circles question

[dementedpixie]

Dd has this question in her holiday homework and is unsure which route to take to work it out. Any ideas?

What an interesting question. The top and bottom are not the same length. Get her to draw 2 isosceles triangles. The top one pointing down from the 8cm length to the centre of the circle, and the bottom one pointing up to meet it, with the unknown length as its base.

See if she can figure it out, but read on if she needs more help.

Draw a vertical line through the triangles. The two triangles on top are now right angle triangles. Use Pythagoras to work out the height.

Take this from 7 to work out the height of the lower one. The hypotenuse is still the radius. So use Pythagoras again.

I think we may have managed it. If you completed it can you say whether you got 6cm as the answer too

That was fun. I got 6 too.

Yes I get 6 cm too.

If your dd is interested, quite a lot of the proofs in circle theories use the radius being the sides of an isosceles triangles and they are fun to figure out for yourself.