Circles • Topic 6 of 7

Chords

A chord is a line segment whose endpoints both lie on the circle. The diameter is the longest possible chord, since it passes through the centre. A radius drawn perpendicular to a chord bisects that chord, a fact used to find chord lengths with the Pythagorean theorem. Equal chords are the same distance from the centre, and chords closer to the centre are longer. While chord computations can get involved, the SAT mostly tests the definitions and the perpendicular-bisector property. Distinguish a chord (both endpoints on the circle) from a tangent (touches at one point) and a secant (crosses at two points).

A circle with a chord and the dashed diameter shownChordschorddiameterA diameter is the longest chord.

✅ Solved examples

1. A segment with both endpoints on a circle is called a:
A chord.
2. What is the longest chord of a circle?
The diameter.
3. A radius perpendicular to a chord does what to it?
Bisects it (cuts it into two equal parts).
4. Of two chords, the one closer to the centre is:
Longer.

✏️ Practice — try these, take hints as needed

1. A line segment with endpoints on the circle is a:
Both ends on the circle.
—
—
Chord.
2. The longest chord in any circle is the:
Through the centre.
—
—
Diameter.
3. A radius drawn perpendicular to a chord bisects it into how many equal parts?
Perpendicular from centre.
—
—
Two.
4. Two chords equally far from the centre are:
Same distance → same length.
—
—
Equal in length.
5. A chord that passes through the centre is also called the:
Longest chord.
—
—
Diameter.

📝 Topic test — 8 questions

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