A circle's centre is connected to its 50 cm long chord by a perpendicular that is 21 cm long. Find the circle's radius.

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Accepted Answer

Given:
- Length of chord = 50 cm
- Perpendicular from center to chord = 21 cm

Step 1: The perpendicular from the center of the circle to the chord bisects the chord.
So, half of the chord = 50/2 = 25 cm.

Step 2: Consider the right triangle formed by the radius (hypotenuse), the perpendicular (one leg), and half the chord (other leg).

Using Pythagoras theorem:
Radius^2 = (Perpendicular)^2 + (Half chord)^2
= 21^2 + 25^2
= 441 + 625
= 1066

Step 3: Therefore, radius = √1066 cm.

Hence, the correct answer is √1066 cm.

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Answer

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