E maths urgent (question on triangle and semicircle)

bonkysleuth SG

In the diagram, the circle with centre at B has a radius (2r + 1) cm. The semicircle with centre at A and the semicircle with centre at C are identical and each has a radius (12-6r)cm. O is the centre of the largest semicircle.

By using pythagoras theorem, form an equation in r and show that it reduces to 18r^2 - 57r + 42 = 0

The questions before this were to find an expression in terms of r for BC and BO. (for guiding purposes)

I need help with this question asap. a big thankssssssssssss!

p.s - sorry for the distorted pic

wee_ws SG

Hi,

Your circles should meet when you draw them :P

BC = (2r + 1) + (12 - 6r) = 13 - 4r.

OB = 2(12 - 6r) - (2r + 1) = 23 - 14r.

OC = 12 - 6r.

Now OB^2 + OC^2 = BC^2, based on the suggestion.

Finally, the result holds upon expansion and simplification.

Thanks!

Cheers,
Wen Shih