Arc Length from a Secant

Answer: With only the length of the secant (88 m) and no information about the radius or the central angle, the length of the corresponding arc cannot be determined.

A secant tells us how far apart the two points of intersection are, but the arc length also depends on how “wide” the circle is (its radius) and the angle subtended at the centre. Without either of those, many different circles can have the same secant length but very different arc lengths.

Example: Imagine two circles, one with a small radius of 5 m and another with a large radius of 50 m. Both can have a secant of 88 m, yet the arc on the small circle might be only a few meters long, while the arc on the large circle could be dozens of meters.

Key Points:

• The secant length alone does not give the radius or central angle.
• Arc length = (radius × central angle in radians).
• Additional data such as radius, diameter, or the angle subtended is required.

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Keywords: secant length, arc length, circumference of arc, circle geometry, CBSE, ICSE, Class X, radius, central angle