Question

a point P is at the 9 unit distance from the centre of a circle of radius 15 unit. The total number of different chord of the circle passing through the point P and have the integral length is

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Answer 1

Answer:

7 different integral values  Chords

13 chord

Step-by-step explanation:

Maximum length of chord = Diameter = 2 * Radius = 2 * 15 = 30 units

as point P is 9 unit distance from center so it will be perpendicular (shortest distance ) for smallest length chord

and by applying Pythagoras theorem for Half length of chord

Half  Length of chord = √(15² - 9²) = √(225 - 81) = √144 = 12 unit

Minimum Length of Chord =  2 * 12 = 24 unit

Minimum length of chord = 24 unit

Maximum length of chord = 30 units

Integral value of chord length are   24 , 25 , 26 , 27 , 28 , 29 , 30

=> 7 chords passing through point having different integral length

24 , 25 , 26 , 27 , 28 , 29 chord will have mirror image chord as well

so total chords = 6 + 6 + 1 = 13