Line segment BA is tangent to the circle. A circle is shown. Secant D B and tangent B A intersect at point B outside of the circ
le. Secant D B intersects the circle at point C. The length of A B is x, the length of B C is 55, and the length of C D is 120. What is the length of line segment BA? Round to the nearest unit.
18 units
65 units
88 units
98 units
18 units
65 units
88 units
98 units
2 answers:
Answer:
98 units
Step-by-step explanation:
There is an equation you can use to solve this. Here it is:
The a squared is the expression for a tangent.
The c(b +c) is the expression for a secant.
This equation applies to all circles that have 1 tangent and one 1 secant.
For this problem, it would help if you draw it out. From the information you can draw a diagram (see attacted picture). It is the picture on graph paper.
All we need to do is plug in the values for the secant and tangent and solve the equation. This is what I did:
a^2 = c(b +c) --------------- Original Equation
AB^2 = BC (DC + BC) --- Equation with line segments
x^2 = 55 (120 + 55) ------ Appropriate values plugged in
x^2 = 55(175) -------------- Parentheses simplified
x^2 = 9,625 ---------------- Right side simplified
sqrt(x^2) = sqrt(9,625) -- Square root both sides
x almost = 98 ------------ Simplified (rounded nearest unit)
The answer is actually 98.107... but we can round that to 98 as the question suggests.
I have also attached pictures of other circle equations that might be included in this unit. Thank my geometry teacher for that! They are the pictures on normal printer paper.
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