Intersecting Chords

Geometry Level 1

The chords FH and EG in a circle intersect at any point in the circle named point D. Segment FD measures 30 units, segment DG measures 36 units, segment DE measures x units and segment DH measures X + 10 units. Find the sum of the length of chords FH and EG.


The answer is 176.

John Paolo Bayaborda by John Paolo Bayaborda , 24, Philippines

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1 solution

FD x DH = ED x DG

30 (x + 10) = 36x

30x + 300 = 36x

300 = 6x

x = 50

x + 10 = 50 + 10 = 60

so by adding the chords, 50+60+36+30 = 176 \boxed{176}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

i still didnt get it.. why FD x DH = ED x DG??

Ram Meena - 7 years ago

Cross chord theorem...

roland casuga - 7 years ago

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