Secants and Arcs of a Circle

Answer: A **secant** is a straight line that cuts a circle at two points, while an **arc** is a part of the circle’s circumference between two points on the circle.

When a line touches a circle at exactly one point, it is a tangent; if it meets the circle at two points, it is a secant. The portion of the circle joining those two intersection points is called the intercepted arc.

Example: Imagine a rope tied at two points on a circular playground fence. The rope follows the fence between those points – that is the arc. If you stretch a straight stick across the playground and it touches the fence at two places, the stick is the secant.

Key Points:

• A secant intersects the circle at exactly two distinct points.
• The intercepted arc is the part of the circumference between those two points.
• Length of an arc = (central angle/360°) × 2πr.
• Secant‑tangent theorem: If a secant and a tangent are drawn from an external point, (external part of secant)² = (external part of secant) × (whole secant).

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Keywords: secant, arc, circle, CBSE, ICSE, Class V, Class X, geometry