Question

A circle with two chords is shown below in the figure. Find the value of x.
X
8
x+12
12
X =

Answer 1

A circle with two chords is given with length X, 8, x-12, 12. Thus, The value of x is 24.

What is the relation between line perpendicular to chord from the center of circle?

If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.

Or

|AC| = |CB|

Using the theorem of intersecting chords

$12x =8(x-12)\\\\12x = 8x - 96\\\\12x - 8x = 96\\\\4x = 96\\\\x = 24$

The value of x is 24.

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