True or False? In O, radius OP intersects chord AC in point B so that AB = 8 units and BC = 8 units. This means that OP is perpendicular to AC.A.TrueB.False

Break Down the Problem

1. Understand the relationship between the radius, the chord, and the perpendicularity.
2. Analyze whether the given segments AB and BC being equal implies that the radius OP is perpendicular to chord AC.

Relevant Concepts

1. A property of chords in circles states that if a radius drawn to a chord bisects the chord, then it is perpendicular to the chord.
2. Given that AB = BC, chord AC is bisected by point B.

Analysis and Detail

1. The lengths of AB and BC are equal (8 units each).
2. Since B is the midpoint of AC, we conclude that chord AC is bisected by OP.
3. According to the property mentioned above, if OP bisects AC, then it must indeed be perpendicular to AC.

Verify and Summarize

1. OP bisects AC at point B where AB = BC.
2. This confirms that OP is perpendicular to chord AC.

Final Answer

A. True