Answer :
Total number of different chords of the circle passing through point P with integer lengths is equal to 7.
As given in the question,
Radius of the circle = 15units
Longest chord of the circle 'diameter' = 2 × 15
= 30units
Point 'P' is 9 units away from the circle.
Consider shortest distance( perpendicular) of point P for shortest chord.
Half length of the chord , shortest distance and radius form right triangle.
(1/2) length of the chord = √15² - 9²
= √225 - 81
= 12units
Length of the chord = 2(12)
= 24 units
Different Chords with integer length = 24, 25, 26, 27, 28 , 29 , 30
Total number of different chords = 7
total number of chords = 6 original + 6 mirror image + 1 longest chord
= 13
Therefore, total chords with different integer length passing through the point P of the circle is 7.
The complete question is :
A point P is at the 9 unit distance from the center of a circle of radius 15 unit. How many total number of different chord of the circle passing through the point P and have the integer lengths?
Learn more about chords here
brainly.com/question/21686011
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