Question

A pole has to be erected at a point on the boundary of a circular park of diameter 13m in such a way that the sum of its distances from two diametrically opposite fixed gates A and B on the boundary is 17m. Is it possible to do so? If yes, at what distance from the two gates should the pole be erected.

• A. $12$ from $A$ & $5$ from $B$
• B. not possible
• C. $13$ from $A$ & $7$ from $B$
• D. $14$ from $A$ & $6$ from $B$

Answer 1

The correct option is A $12$ from $A$ & $5$ from $B$

As per question ,

$x+y=17$

And by Pythagoras theorem,

x${}^2$+y${}^2$ = 13 ( Angle in a semicircle is right angle)

Solving we get $x=12$ and $y=5$ .