Question

If FC=33cm and CH=13cm the what is the length of FH

circle with a triangle and has a right angle

Answer 1

In the context of a right triangle inscribed in a circle (circumcircle), where \( FC \) is the radius of the circle, and \( CH \) is a segment that goes from a vertex (C) to the midpoint of the hypotenuse (FH), we want to find the length of \( FH \).

If \( FC \) is the radius (\( R \)) of the circumcircle and \( CH \) is the altitude from vertex \( C \) to the hypotenuse \( FH \), we can use the relationship of segments in a right triangle inscribed in a circle:

Using the relationship of a right triangle inscribed in a circle:
\[
R = \frac{c}{2}
\]
where \( c \) is the hypotenuse.

In your case:
- The radius \( FC \) is given as \( 33 \text{ cm} \), so \( R = 33 \text{ cm} \).
- The segment \( CH \) represents the height from vertex \( C \) to hypotenuse \( FH \) and is given as \( 13 \text{ cm} \).

To find the length of \( FH \):
Using the property of the circumradius of a right triangle:
\[
R = \frac{1}{2} FH \implies FH = 2R
\]
Substituting the values:
\[
FH = 2 \times 33 = 66 \text{ cm}
\]

So, the length of \( FH \) is \( 66 \text{ cm} \).