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Given : Chords A C and B D intersect at point E. Length of Different segments is given in terms of x
To find : Length of chord BD
Solution:
Chords A C and B D intersect at point E.
=> AE * CE = BE * DE
AE = x
CE = x + 12
BE = x + 2
D = x + 5
=> x(x + 12) = (x + 2)(x + 5)
=> x² + 12x = x² + 7x + 10
=> 5x = 10
=> x = 2
BD = BE + DE
= x + 2 + x + 5
= 2x + 7
putting x = 2
=> BD = 2 (2) + 7
Applying the intersecting chord theorem, the length of segment CE in is: 2.5 units.
In geometry, the intersecting chords theorem is the theorem that defines the relation of the four line segments formed when two chords of a circle intersect each other at a point in the circle.
According to the intersecting chords theorem, the products of the lengths of the line segments that are formed on each chord are congruent or equal to each other.
In the diagram given, we have chords AC and BD intersecting at point E to form the following line segments:
BE = BD - DE = 7 - 2 = 5 units
DE = 2 units
AE = 4 units
CE = ?
Based on the intersecting chord theorem, we have:
(BE)(DE) = (AE)(CE)
Plug in the values
(5)(2) = (4)(CE)
10 = 4(CE)
Divide both sides by 4
10/4 = 4(CE)/4
2.5 = CE
CE = 2.5 units
Thus, applying the intersecting chord theorem, the length of segment CE in the circle given is: 2.5 units.
Learn more about the intersecting chord theorem on:
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