calculate the length of a chord which is at a distance 12 cm from the centre of a circle of radius 13cm
Answers
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Given,
The distance of chord from centre = 12 cm
Radius = 13 cm
To find,
The length of the chord.
Solution,
The length of the chord will be 10 cm.
We can easily solve this problem by following the given steps.
Now,
Let's take the centre of the circle to be A, the chord to be BC and the point on the chord from the centre to be D.
So,
AB = AC = 13 cm (radius of the circle)
AD = 12 cm (distance of the chord from the centre)
The two right-angled triangles will be formed. ( ∆ ADB and ∆ ADC)
Using Pythagoras theorem in ∆ ADB,
AB² = AD² + BD²
BD² = AB² - AD²
BD² = (13)² - (12)²
BD² = 169 - 144
BD² = 25
BD = √25
BD = 5 cm
The chord is BC that is the sum of BD and DC.
DC will be equal to BD as the AC is equal to AB and AD is common.
BD = DC = 5 cm
Length of the chord, BC = BD + DC
Length of the chord = (5+5) cm
Hence, the length of the chord will be 10 cm.