The terrorist’s eye

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The terrorist’s eye

by sanju09 » Fri Feb 19, 2010 3:25 am
A soldier standing on the center of a circular community hall, which is surrounded by bullet proof and transparent glass walls, observes that a terrorist who is standing at a distant point from the community hall makes two bullet fires towards the hall, each in a different direction, such that each of the two bullets fired slide past tangentially with the walls. What is the angle subtended by the direct distance between the two points on the wall that were bullet hit, at the eye of the soldier?

(1) The angle subtended by the direct distance between the two points on the wall that were bullet hit, at the eye of the terrorist, is half that of what is subtended at the eye of the soldier.

(2) The terrorist's eye, the soldier's eye, and the two bullet hit points on the glass wall, are all in the same plane parallel to the base of the community hall.
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by harsh.champ » Fri Feb 19, 2010 5:28 am
sanju09 wrote:A soldier standing on the center of a circular community hall, which is surrounded by bullet proof and transparent glass walls, observes that a terrorist who is standing at a distant point from the community hall makes two bullet fires towards the hall, each in a different direction, such that each of the two bullets fired slide past tangentially with the walls. What is the angle subtended by the direct distance between the two points on the wall that were bullet hit, at the eye of the soldier?

(1) The angle subtended by the direct distance between the two points on the wall that were bullet hit, at the eye of the terrorist, is half that of what is subtended at the eye of the soldier.

(2) The terrorist's eye, the soldier's eye, and the two bullet hit points on the glass wall, are all in the same plane parallel to the base of the community hall.
1st of all I have to admit its a bit difficult word translation problem.
Important point to note:-The bullets will make a 90 degree angle with the line joining the radius and the pt. of tangency.

Let the pt. of tangency be T and T'.
Centre of the circle be C.
Point where terrorist is standing be P.
We have CTPT' as a quadrialteral.
Sum of the angles = 360 degrees.
Also, as a rule of geometry- "The bullets will make a 90 degree angle with the line joining the radius and the pt. of tangency"
Hence, (<TPT)' +(<TCT') = 180
We have to find <TCT'.

Statement 1:-<TPT' = 1/2(<TCT')
But,(<TPT)' +(<TCT') = 180.
Hence,statement 1 is sufficient.

Statement 2:-This statement is self-implied.Hence Insufficient.
(I am assuming that we are not considering 3-D geometry.)

Answer is A.
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