Radius of the circle is 10cm and distance of chord from the centre is 6 cm. Hence the length of the
chord is…………
Answers
The radius of the circle is 10cm and the distance of the chord from the centre is 6 cm. Hence the length of the chord is 16 cm.
Given,
The radius of the circle = 10 cm
Distance of chord from the centre = 6 cm
To find,
The length of the chord.
Solution,
The length of the chord will be 16 cm.
We can easily solve this problem by following the given steps.
Now, let's take the centre of the circle to be A and the chord to be BC.
Let's take the point on the chord from the centre to be D and BD to be x cm.
According to the question,
AB = AC = 10 cm (radius)
AD = 6 cm
The triangle ADB is right-angled.
Using Pythagoras theorem in ∆ADB,
AB² = AD² + BD²
(10)² = (6)² + (x)²
100 = 36 + x²
100 - 36 = x² ( Moving 36 from tbe right-hand side to the left-hand side will result in the change of sign from plus to minus.)
64 = x²
x² = 64
x = √64
x = 8 cm
Now, BD and DC are equal because the line from the centre is perpendicular is dividing the chord into two equal parts.
BD = DC = 8 cm
The length of the chord, BC = BD + DC
The length of the chord = (8+8) cm
The length of the chord = 16 cm
Hence, the length of the chord of the circle is 16 cm.
the length of the chord is 16 cm