Question

Qingyun has constructed a circle with center O and chords AB and CD that intersect at point E inside the circle. According to her measurements, segment a=13 mm, segment b=20 mm, and segment d=10 mm. What is the length of chord CD ? (1 point) Responses Chord CD is 260 mm. Chord upper C upper D is 260 mm. Chord CD is 26 mm. Chord upper C upper D is 26 mm. Chord CD is 36 mm. Chord upper C upper D is 36 mm. Chord CD is 33 mm.

Answer 1

To find the length of chord CD, we can use the intersecting chords theorem, which states that if two chords AB and CD intersect at point E inside the circle, then:

\[ AE \times EB = CE \times ED \]

Given the segments:
- \( AE = a = 13 \) mm
- \( EB = b = 20 \) mm
- \( CE = c \) (unknown)
- \( ED = d = 10 \) mm

Substituting the known values into the equation:

\[ AE \times EB = CE \times ED \]

This results in:

\[ 13 \times 20 = c \times 10 \]
\[ 260 = 10c \]
\[ c = \frac{260}{10} \]
\[ c = 26 \]

Now that we have \( CE = 26 \) mm, we can find the length of chord CD, which is:

\[ CD = CE + ED = c + d \]
\[ CD = 26 + 10 \]
\[ CD = 36 \] mm

Therefore, the length of chord CD is 36 mm.

The correct response is: **Chord CD is 36 mm.**