Question

Paul, Lara, and Carry are sitting on the boundary of a circular field such that each one of them is sitting $20\sqrt{3}$ m away from the other. Paul pushes a toy car towards Lara. How far is the car from Carry when it is midway? (Assume that the car is traveling in a straight line.)

Answer 1

Let's understand the situation with the help of a figure.

We have to find the distance CD.
ABC is an equilateral triangle.
So, AD is half of AB.

Using the Pythagorean theorem,
In ${△}^{\text{le}}$ ACD,
${\text{CD}}^2$ + ${\text{AD}}^2$ = ${\text{AC}}^2$

AD = $\text{10}\sqrt{3}$
AC = $\text{20}\sqrt{3}$

${\text{CD}}^2$ + $(\text{10}\sqrt{3}{)}^2$ = $(\text{20}\sqrt{3}{)}^2$

${\text{CD}}^2$ + 300 = 1200

${\text{CD}}^2$ = 1200 – 300 = 900

CD = $\sqrt{900}$

CD = 30 m