If $\mathrm{AB}$ and $\mathrm{CD}$ are diameters of circle $t$ that intersect at the center, what is the measure of angle $\angle \mathrm{ACD}$?

• A. $90°$
• B. $180°$
• C. $60°$
• D. $45°$

Answer: (A)

Verified step by step guidance

1. Recognize that AB and CD are diameters of the same circle t, so they both pass through the center of the circle, which we'll call O.
2. Since AB and CD are diameters, points A and B lie on the circle opposite each other, and points C and D also lie opposite each other, with O as the midpoint of both segments.
3. Because AB and CD intersect at the center O, the segments AB and CD are straight lines crossing at O, forming four angles around O.
4. Note that diameters of a circle are straight lines, so AB and CD are straight lines intersecting at O, and the angle formed between these two diameters at the center is the angle between the lines AB and CD.
5. Since AB and CD are diameters intersecting at the center, the angle between them (angle ACD) is the angle between two chords intersecting at the circumference, which can be found using properties of circles and inscribed angles.