P is a point on the segment joining the feet of two vertical poles of heights a and b. The angles of elevation of the tops of the poles from P are 45° each. Then, the square of the distance between the tops of the poles is

1) (a² + b²) / 2

2) (a² + b²)

3) 2 (a² + b²)

4) 4 (a² + b²)

Solution: (3) 2 (a² + b²)

OA = a, AB = b, DE = a + b, CE = b – a

l = (a + b)² + (b – a)²

= a² + b² + 2ab + b² + a² – 2ab

= 2a² + 2b²

= 2 (a² + b²)