Length of chord in circle

Question

In Figure 3, arc CD is a semicircle. AB is perpendicular to CD, BC = 3, BD = 4. Then the length of AB =

a) 3.25 b) 4.56 c) 3.46 d) 7.00

Bernd · Answer 1 · 2014-01-08T15:46:51.693

3

You have a rectangular triangle ACD. Use Euklids sentence (h^2 = p*q = 12 and therefore AB = sqare root of 12 = 3,46...

edited Jan 08 '14 at 15:46

answered Jan 08 '14 at 15:27

Bernd

I don't know why but it is not appearing. I just made my account here. – Mubasher Ahmed Jan 08 '14 at 15:28
Now I see it, thanks. This means you have a rectangular triangle ACD. Use Euklids sentence (h^2 = p*q = 12 and therefore AB = sqare root of 12 = 3,46... – Bernd Jan 08 '14 at 15:32
1

@Bernd: Please edit your Answer now to include that solution. – hardmath Jan 08 '14 at 15:36

mathlove · Accepted Answer · 2014-01-08T15:35:01.120

1

HINT :

Note that $\angle CAD=90^\circ$, and so $AC^2+AD^2=CD^2$.

Letting $AB=x$, since $$AC^2=x^2+3^2, AD^2=x^2+4^2, CD^2=7^2$$

you'll get an equation of $x$ as $$7^2=9+x^2+x^2+16\iff x^2=12.$$

edited Jan 08 '14 at 15:35

answered Jan 08 '14 at 15:29

mathlove

2 Answers2