Length of BD is 11 units.
The intersecting chords theorem or just the chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
Let length of AE be x
By intersecting chords theorem,
AE(ED) = BC(DE)
x(x + 12) = (x +2)(x +5)
x² + 12x= x² + 7x + 10
5x = 10
x = 2
BD = BE + DE
= x + x +7
= 2x + 7
= 2(2) + 7
= 11 units
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