One chord of a circle is known to be of length 10cm. The radius of this circle may be:

One chord of a circle is known to be of length 10cm. The radius of this circle may be:

A
5 cm
B
Greater than 5cm
C
Greater than or equal to 5cm
D
All of these

Solution:

Given,
Length of one chord of a circle = 10cm.
Consider, AB the chord of circle O and OA is the radius of it where OA = x.

Draw OP perpendicular to AB as shown in the figure. Hence, AB = 10 cm. …[Given]

PA = \frac{10}{2} = 5 cm

Consider

Δ

POA,

{AO}^{2} = {PA}^{2} + {OP}^{2}

x^{2} = 5^{2} + {OP}^{2}

x = \sqrt{5^{2} + {OP}^{2}} . . . . . . (1)

5^{2} + {OP}^{2} > 5^{2}

.
If OP = 0, them x = 5 cm.
If OP ≠ 0, then x > 5 cm
So from equation (1), we get x ≥ 5.
Therefore, option 4 is correct.

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