in the square ABCD,AB=24. The diagonals of the square intersect at point P. A circle centered at point P with diameter 26, intersect AB at E and F . Find the length of EF.
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Given : in the square ABCD,AB=24.
The diagonals of the square intersect at point P. A circle centered at point P with diameter 26, intersect AB at E and F .
To Find : the length of EF.
Solution:
ABCD is square
AB = BC = CD = AD = 24
AC = BD = Diagonal = 24√2
AP = BP = CP = DP = 12√2
Draw a perpendicular PM ⊥ AB
PM = 12
PE = PF = 13 ( radius of circle , diameter = 26 => radius = 13)
EM² = PE² -PM² = 13² - 12² = 5² => EM = 5
FM² = PF² -PM² = 13² - 12² = 5² => FM = 5
EF = EM + FM = 5 + 5 = 10
the length of EF. = 10
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