semicircle

[fruti_yum]

attached is the diagram!

can't figure out for the life of me!

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A. 5½ ft
B. 7½ ft
C. 8 ½ ft
D. 9½ ft
E. 10 ft

oa after discussion

[Nermal]

I think it's b (7.5ft.)

this is how I got there:

first we know the d=20, therefore r=10

the lane is supposed to be 12ft wide with equal distance from the left and right side, so this gives us a distance of 6ft from O in both directions.

Now we are supposed to find out how "tall" vehicles may be at the most.

This is the point I labelled "max. height" on the upper right side.

This now gives us a triangle with the base of 6ft. (half the lane) and a hypothenuse of 10ft. (it's the radius)

This is a 3-4-5 triangle with a factor of 2.
10=5*2
6=3*2

x=4*2=8

Now the maximum height of the vehicle should be 1/2foot smaller. Thus: 8ft.-1/2ft = 7.5ft.

This leaves us with answer b.

[Nermal]

Can you please give OA?