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More Lessons for High School Regents Exam

Math Worksheets

High School Math based on the topics required for the Regents Exam conducted by NYSED.

**Theorem on Circles and Chords**

In a circle, a radius perpendicular to a chord bisects the chord.

In a circle, a radius that bisects a chord is perpendicular to the chord.

In a circle, the perpendicular bisector of a chord passes through the center of the circle.

The following diagram gives the perpendicular bisector theorem for the chords in a circle. Scroll down the page for more examples and solutions.

**Theorem on Congruent Chords**

In a circle, or congruent circles, congruent chords have congruent arcs. (converse) In a circle, or congruent circles, congruent arcs have congruent chords.

The following diagram gives the theorem for congruent chords. Scroll down the page for more examples and solutions.

**Arcs and Chords**

Radius drawn perpendicular to a chord bisects the chord and the arc

**Circles: Arcs and Chords Pt 1**

In a circle, or congruent circles, congruent chords have congruent arcs. (converse) In a circle, or congruent circles, congruent arcs have congruent chords. A diameter that is perpendicular to a chord bisects the chord and its arc

**Circles: Arcs and Chords Pt 2**

In a circle, or congruent circles, congruent chords have congruent arcs. (converse) In a circle, or congruent circles, congruent arcs have congruent chords. A diameter that is perpendicular to a chord bisects the chord and its arc

**Circles: Arcs and Chords Pt 3**

In a circle, or congruent circles, congruent chords have congruent arcs. (converse) In a circle, or congruent circles, congruent arcs have congruent chords. A diameter that is perpendicular to a chord bisects the chord and its arc

**Arcs and Chords**

If a diameter is perpendicular to a chord, then it bisects the chord and its arc.

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