Find the values of \angle ABC, AC, and OB in the first diagram.

INSIGHT

Solution:

• The diagram shows a circle with center O and diameter AC.
• The length of the diameter is given as 2 cm.
• OB: OB is the radius of the circle. The radius is half the diameter, so OB = AC / 2 = 2 cm / 2 = 1 cm.
• \angle ABC: Since AC is the diameter, the angle subtended by the diameter at point B on the circumference is a right angle. Therefore, \angle ABC = 90 degrees.
• AC: AC is the diameter of the circle, and its length is given as 2 cm.

Final Answer:

\angle ABC = 90^{\circ}

AC = 2 \text{ cm}

OB = 1 \text{ cm}