Geometry
posted by Carolina
Two secants are drawn to a circle from an external point. The external secant length on the first secant is 12 and the internal segment length is 3x +1. The external secant length on the second secant is 15 and the two internal segment length is 3x1. Solve for (x) to determine the lengths of the two internal segments of the secants.

MathMate
I assume you meant:
"...and the second internal segment length is 3x1..."
First, recall that a secant from an external point P cutting a given circle at A and B has the following properties:
PA*PB = PA'*PB' = PT^2....(1)
where A'B' are two other points of intersection of a second secant, and T is the point of tangency.
For the given case,
PA=12, PB=12+3x+1=13+3x
PA'=15, PB'=15+3x1=14+3x
From equation (1),
12(13+3x)=15(14+3x)
which gives
x=54/9=6, or
3x+1=17, 3x1=19 (impossible).
Unless I made a mistake somewhere, I suggest you recheck the question and proceed to solve for x in the same way above.
Respond to this Question
Similar Questions

Geometry and Algebra
AB is a diameter of a circle with centre O. P is on BA extended, and PT is tangent to the circle. Use the corollary to the Intersecting Secants Property to prove that PT is perpendicular to OT. Here is the diagram (Without the dashes … 
math
Two secant segments are drawn to a circle from a point outside the circle. The external segment of the first secant segment is 8 centimeters and its internal segment is 6 centimeters. If the entire length of the second secant segment … 
geometry 1
a secantsecant angle intercepts arcs that are 3/5 and 3/8 respectively. Find the measure of the secantsecant angle. 
geometry
Two secant segments are drawn to a circle from a point outside the circle. The external segment of the first secant segment is 8 centimeters and its internal segment is 6 centimeters. If the entire length of the second secant segment … 
geometry
Two secant segments are drawn to a circle from a point outside the circle. The external segment of the first secant segment is 8 centimeters and its internal segment is 6 centimeters. If the entire length of the second secant segment … 
Geometry
A secant and a tangent to a circle intersect in a 42 degree angle. The two arcs of the circle intercepted by the secant and tangent have measures in a 7:3 ratio. Find the measure of the third arc. If someone could help me figure out … 
Geometry
Two secants of a circle meet in a point out side to the circle. One Secant has 4 and x. The other Secant is 5 and 4. What will be x? 
Math (Secant Lines)
Consider the function f(x)=sqrt(x) and the point P(4,2) on the graph of f? 
Math (Calculus) (mean value theorem emergency)
Consider the graph of the function f(x)=x^2x12 a) Find the equation of the secant line joining the points (2,6) and (4,0). I got the equation of the secant line to be y=x4 b) Use the Mean Value Theorem to determine a point c in … 
Geometry
If a tangent segment and a secant segment are drawn to a circle from the same point, the external part of the secant segment is longer than the tangent segment. True or False?