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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.

More Lessons for High School Regents Exam

Math Worksheets

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

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.

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.

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

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

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

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

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

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