In the circle if two secants are drawn to a circle from one common exterior point, then the product of the two external segment and the total length of each segment is equal. The value of the x is 2 units.
Given information
In the given figure two line segment AD and AE intersect the circle at point B and C. In which,
[tex]BE=x+1\\CE=x+4\\DE=1=x+4=x+5\\AE=11+x+1=x+12[/tex]
What is intersecting secants theorem?
In the circle if two secants are drawn to a circle from one common exterior point, then the product of the two external segment and the total length of each segment is equal.
Therefore for the given segments,
[tex]BE\times AE=CE\times DE[/tex]
Put the values,
[tex](x+1)\times (x+12)=(x+4)\times (x+5)\\x^2+x+12x+12=x^2+4x+5x+20\\13x+12=9x+20\\4x=8\\x=2[/tex]
Thus the value of the x is 2 units.
Learn more about the intersecting secants theorem here;
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