Question

Proof

Answer 1

the two angles that are marked in the diagram - do you agree that they are equal?

Answer 2

I marked them o-o

Answer 3

ok, good :)
now, do you also agree that angle ABC = 90 degrees?

Answer 4

I would, but I don't know why.

Answer 5

because it is the angle subtended by a diameter

Answer 6

oh. the semicircle thing

Answer 7

next angle DAC = 90 degrees also - do you know why?

Answer 8

radius-tangent angle is 90?

Answer 9

good

Answer 10

now in triangle ABC, what is the cos of angle BAC equal to?

Answer 11

I haven't learned that yet. Don't you just prove that the 2 triangles are similar?

Answer 12

yes - you can also use similar triangles for this

Answer 13

so in triangles ABC and DAC we have shown that they have two angles equal, therefore their third angle must also be equal therefore they are similar

Answer 14

now you should be able to use ratios of similar triangles to get the desired proof

Answer 15

(ratios of corresponding sides)

Answer 16

hopefully you can prove the rest from here?

Answer 17

sure.

Answer 18

gr8 - good luck! :)

Answer 19

ty

Answer 20

yw :)