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Difficulty: 2/102023 NMTC 2023 (QII-21)

A chord of length 24cm is at distance of 5cm from the center of circle. The radius of the circle is ________.

Guide / Hint

Hint 1: A perpendicular line from the center bisects the chord of length 24 cm into two segments of 12 cm.

Hint 2: Form a right triangle with the radius, the perpendicular distance (5 cm), and half of the chord (12 cm).

Hint 3: Use the Pythagorean theorem to calculate the hypotenuse, which is the radius.

Solution

Step 1 (Setup and Chord Bisector Property): Draw a circle with center . A chord of length 24 cm is drawn. The distance from the center to the chord is the perpendicular segment cm. Since a perpendicular line from the center to a chord bisects the chord:

Step 2 (Apply Pythagorean Theorem): In the right-angled triangle , the hypotenuse is the radius , the base is cm, and the altitude is cm. By the Pythagorean Theorem:

Step 3 (Conclusion): The radius of the circle is exactly 13 cm.

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