Mathematics
The radius of a circle is 13 cm and length of chord is 10 cm. The shortest distance between chord and the centre is:
12 cm
15 cm
16 cm
18 cm
Circles
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Answer
Let AB be chord of length = 10 cm
Radius OA = 13 cm
Let OD be the perpendicular distance from the center to the chord, it bisects the chord into two equal parts:
AD = DB = = 5 cm
In triangle OAD,
According to the Pythagorean Theorem:
OA2 = OD2 + AD2
132 = OD2 + 52
169 = OD2 + 25
OD2 = 169 - 25
OD2 = 144
OD = = 12 cm
The shortest distance between the chord and the center is 12 cm.
Hence, option 1 is the correct option.
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