MATHCOUNTS PROBLEM 223

Mathematics
Tutor: None Selected Time limit: 1 Day

Two chords of a circle intersect. The point of intersection divides the first chord into two segments of length 5 cm and 8 cm and divides the second chord into two segments, one which has length 4 cm. How long is the second chord?

Jun 7th, 2015

When two chords intersect each other inside a circle, the products of their segments are equal.

Let the length of unknown segment of the second  chord be x.

So, 

5*8 = 4*x

40 = 4x

4x = 40 

x = 40/4

x = 10 cm


Length of the second chord = 4 + x = 4 + 10 = 14 cm

Jun 7th, 2015

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