Grade 10 — Circles (Chords/Tangents/Arcs)

Parts of a Circle

A **circle** is a set of points in a plane that are all a fixed distance from a central point. Let's define some key parts:

A **chord** is a line segment that connects two points on a circle.
A **diameter** is a special chord that passes through the center of the circle.
A **tangent** is a line that touches the circle at exactly one point. The radius drawn to the point of tangency is perpendicular to the tangent line.
An **arc** is a portion of the circle's circumference. The measure of an arc is equal to the measure of the central angle that intercepts it.
A **sector** is a region of a circle bounded by two radii and an arc.

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Watch this video to visualize the relationships between chords, tangents, and arcs! 🎥

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Solve these problems based on the properties of circles!

1) A chord is 8cm long in a circle with a radius of 5cm. How far is the chord from the center?

2) A tangent segment from an external point is 12. The distance from the external point to the center is 13. What is the radius?

3) The central angle for an arc is $60^\circ$. What is the arc's measure?

4) A diameter is 10cm. What is the radius?

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