» The two chords intersect inside the circle, then the product of the measure of the segment of one chord is equal to the product of the measures of the segment of the other chord.
[tex](y)(12) = (4)(9)[/tex]
[tex]12y = 36[/tex]
[tex]\frac{12y}{12}= \frac{36}{12} \\ [/tex]
[tex]y = 3[/tex]
[tex] \therefore [/tex] The value of y is 3units.
[tex] \rm [/tex]
Find x:
» The secant and tangent line intersect outside the circle, then the square of the length of tangent is equal to the product of the lengths of one secant and external secant.
[tex] {18}^{2} = (x)(12 + 3 + x)[/tex]
[tex]324 = (x)(12 + 3 + x)[/tex]
[tex]324 = (x)(15 + x)[/tex]
[tex]324 = x^2 + 15x [/tex]
[tex]x^2 + 15x - 324 = 0[/tex]
» Solve the quadratic equation by factoring. Use the positive solution.
Answers & Comments
✒️CIRCLE
[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
[tex] \large\underline{\mathbb{ANSWERS}:} [/tex]
[tex] \qquad\Large\rm \:\: y=3 \: units [/tex]
[tex] \qquad\Large\rm \:\:x=12\: units [/tex]
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[tex] \large\underline{\mathbb{SOLUTIONS}:} [/tex]
Find y:
» The two chords intersect inside the circle, then the product of the measure of the segment of one chord is equal to the product of the measures of the segment of the other chord.
[tex] \therefore [/tex] The value of y is 3 units.
[tex] \rm [/tex]
Find x:
» The secant and tangent line intersect outside the circle, then the square of the length of tangent is equal to the product of the lengths of one secant and external secant.
» Solve the quadratic equation by factoring. Use the positive solution.
[tex] \therefore [/tex] The value of x is 12 units.
[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
I HOPE THIS HELPS :)