Triangle in a semicircle

[Jaspworld]

Suppose C lies on a semicircle with diameter AB=10 cm. Visualize C moving along the semicircle. As it moves, the length of a, b, h, x ,and y change.

Image is located at http://www.freewebsite.0nyx.com/images/triangle1

a) Determine the value(s) of x such that the triangle with side lengths a,b, and h is a right triangle

b) Determine the value(s) of x such that the triangle with the side lengths h, x, and y is a right triangle

c) How do the triangles you found in parts a and b compare with triangle ABC? Explain.

 

[Denis]

Sooooo....what are your answers?

 

[Jaspworld]

Well..

I don't really get this question. However, I have the answers if it helps:
3.82 and 6.18 for both a and b.
HELP!

 

[stapel]

I have the answers if it helps:
3.82 and 6.18 for both a and b.

Parts (a) and (b) have the same answer...? And to which variables do "3.82" and "6.18" correspond?

a) As given, segments a, b, and h do not form a triangle (h is inside the angle formed by sides a and b), so this is not answerable.

              *    C
       *          |  *        Side "a" is segment BC.
    *           h |     *     Side "b" is segment AC.
   *              |      *
  *           O   |       *
A *-----------*---N-------* B
  |<------x------>|<--y-->|
  |<---------10---------->|

b) Same problem as with part (a).

c) Until (a) and (b) make sense, this can't be answered either.

Eliz.

 

[Jaspworld]

huh..

Maybe it is impossible but that is what the book says. My teacher will check up on this soon.

 

[Jaspworld]

It's possible..

The question's a little tricky but it's possible.
We can prove that a(sq.)=cy, b(sq.)=cx, and h(sq.)=xy using similar triangles first.

Part a.)
Then we have three cases: a(sq.)+b(sq).=h(sq.), b(sq.)+h(sq.)=a(sq.), and a(sq.)+h(sq.)=b(sq.)[not possible].
We solve in terms for x and use y=10-x. Using quadratic formula we get the answers.

Now, how do you solve part c.
:wink: [/code]