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Mathematics

Grade9

Easy

Question

Find the value of j in the figure.

14
12
11
16

hint Hint:

By using the secant theorem, if two secants intersect in the exterior of a circle, then the product of the measures of one secant segment is equal to the product of the measures of the other secant and its external secant segment

The correct answer is: 16

By using the secant theorem, if two secants intersect in the exterior of a circle, then the product of the measures of one secant segment is equal to the product of the measures of the other secant and its external secant segment
In this question we have to extend the line MB such that it connects to the circle making a secant.
By using the theorem, we can say that
$M A squared space equals space M L space cross times space M J$
In this question we are given that MA = $6$ , ML = $2$ and MJ = $2 plus j$ and we have to find $j$ . We can find it by putting the values in the above formula
$6 squared space equals space 2 cross times left parenthesis 2 space plus space j right parenthesis$
=> $j space equals 16$
So, the value of $j$ is $16$

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