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# The Diameter and a Chord of a Circle Have a Common End-point. If the Length of the Diameter is 20 Cm and the Length of the Chord is 12 Cm, How Far is the Chord from the Centre of the Circle? - ICSE Class 10 - Mathematics

ConceptChord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord

#### Question

The diameter and a chord of a circle have a common end-point. If the length of the diameter is 20 cm and the length of the chord is 12 cm, how far is the chord from the centre of the circle?

#### Solution

AB is the diameter and AC is the chord.

Draw OL ⊥ AC
Since OL ⊥ AC and hence it bisects AC, O is the centre of the circle.
Therefore, OA = 10 cm and AL = 6 cm
Now, in Rt. ΔOLA,
AO^2 = AL^2  + OL^2
⇒ 10 ^2 = 6^2 + OL^2

⇒  OL^2  = 100  - 36 = 64
⇒ OL = 8 cm
Therefore, chord is at a distance of 8 cm from the centre of the circle.

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Solution The Diameter and a Chord of a Circle Have a Common End-point. If the Length of the Diameter is 20 Cm and the Length of the Chord is 12 Cm, How Far is the Chord from the Centre of the Circle? Concept: Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord.
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