Consider the following circle with center at point O.
Circle O with points R, U, S and T on the circle. Segments SR and TU pass through point O. Segment RT is also shown in the diagram.

Identify one radii, one diameter, and one chord of the circle. Justify your answers.

Given:

Given that the circle O with points R, U, S and T on the circle. Segments SR and TU pass through point O. Segment RT is also shown in the diagram.

We need to determine the radii, diameter and chord of the circle.

Radii of the circle:

A radius of a circle is line from the center of the circle to the circumference of the circle.

From the diagram, the radius of the circle are OR, OT, OS and OU.

Diameter of the circle:

The diameter of the circle is the straight line that passes through the center of the circle and its endpoints lie on the circle.

Thus, from the diagram, the diameter of the circle are TU and RS.

Chord of the circle:

A chord of the circle is a straight line whose endpoints lie on the circle.

Thus, from the figure, the chord of the circle is TR.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

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step-by-step explanation: