SOLUTION: A road is tangent to a circular lake. Along the road and 12 miles from the point of tangency. Another road opens towards the lake. From the intersection of the two roads to the pe
Algebra.Com
Question 1146428: A road is tangent to a circular lake. Along the road and 12 miles from the point of tangency. Another road opens towards the lake. From the intersection of the two roads to the periphery of the lake, the length of the new road is 11 miles. If the new road will be prolonged across the lake, find the length of bridge to be constructed.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
When you draw the figure for this problem, what you have is a circle with a tangent (line from an external point just touching the circle) and a secant (line from the same external point, passing through the circle.)
The operating principle here (which can be proved using similar triangles) is that the square of the length of the tangent is equal to the product of the length of the external part of the secant and the length of the entire secant.
In this problem, the 12 miles is the tangent length, the 11 miles is the length of the external part of the secant. The unknown x is the length of the part of the secant inside the circle -- the bridge that is to be built.
Applying the basic principle with those numbers gives us
I leave it to you to do the calculations.
RELATED QUESTIONS
A road is tangent to a circular lake. Along the road and 12 miles from the point of... (answered by Alan3354)
Town A is 9 miles from town B, and 12 miles from town C. A road connects towns B and C... (answered by solver91311,richwmiller)
a car travels along an inclined road, in the desert, at 45 mph for 6 hours, from point a... (answered by Alan3354)
Along a road, spot X and spot Y are 1150m apart. Ann walks along the road from X to Y at... (answered by josgarithmetic)
An existing road passing along the circumference of the circular lake. A proposed bridge... (answered by ikleyn)
A van full of storm chasers is driving along a straight road at 61 miles per hour in... (answered by ankor@dixie-net.com)
A certain large city has a circular road around the city and a road directly through... (answered by richwmiller)
There is a 1 m wide road. Two turtles start to crawl down the road from opposite... (answered by greenestamps)
a man drives 500 miles along an inclined road of 20 degrees to horizontal. How high above (answered by solver91311)