Question

In the figure shown, segment B D is a diameter of circle C.



A figure.Short description, A figure.,Long description,
The figure shows circle A with diameter B D. Point C is on the circle, above the diameter. Point E is on the circle, below the diameter. Angle B C D is inscribed in the circle.


Question
Move options to the blanks to show that angle B C D is a right angle.

Response area with 3 blank spaces
Because segment B D is a diameter of the circle,
Blank space 5 empty
.


Therefore, the measure of angle B C D equals 90º because a(n)
Blank space 6 empty
is half the measure of its
Blank space 7 empty
.

Answer 1

To fill in the blanks and show that angle \( \angle BCD \) is a right angle, you can use the following statements:

**Response area with 3 blank spaces:**
Because segment \( BD \) is a diameter of the circle,
**Blank space 5:** \( C \) is on the circle.
Therefore, the measure of angle \( BCD \) equals 90º because a(n)
**Blank space 6:** inscribed angle
is half the measure of its
**Blank space 7:** intercepted arc.

So, the complete response would be:

Because segment \( BD \) is a diameter of the circle,
\( C \) is on the circle.
Therefore, the measure of angle \( BCD \) equals 90º because a(n) inscribed angle is half the measure of its intercepted arc.