Question

Three moons are in the same circular orbit around a planet. The moons are each 120,000 kilometers from the surface of the planet, located at points A, B, and C. The planet is 60,000 kilometers in diameter and m?ABC=90?. How far is point A from point C?

Answer 1

This situation can be assumed as 2 concentric circles and the moons A, B and C are on the outer circle.

The inner circle is the periphery of the planet.

It is given that $\angle ABC$ is $90^\circ$ i.e. the chord AC subtends an angle of $90^\circ$ on the outer circle.

It is possible if and only if the arc AC is actually the diameter of outer circle.

To find the distance between A and C, we need to find out the diameter of outer circle.

Please refer to the attached figure in the answer area.

$AC = AP + PQ + QC$

AP is the distance of moon A from the surface of planet.

AP = 60000 km

PQ is the diameter of inner circle.

PQ = 120000 km

QC is the distance of moon C from the surface of planet.

QC = 60000 km

$\Rightarrow AC = 60000 + 120000 + 60000\\\Rightarrow AC = 300000\ kms$

Hence, distance between moons A and C is 3,00,000 kms.