First slide

Equation of line in Straight lines

Question

Let $A_{0} A_{1} A_{2} A_{3} A_{4} A_{5}$ be a regular hexagon inscribed in a circle of unit radius then the product of the lengths of the line segments $A_{0} A_{1}, A_{0} A_{2}$ and $A_{0} A_{4}$ is

Moderate

Solution

The vertices of the hexagon be as shown in
the figure
$\begin{aligned} {(A_{0} A_{1})}^{2} = \frac{1}{4} + \frac{3}{4} = 1 \\ {(A_{0} A_{2})}^{2} = \frac{9}{4} + \frac{3}{4} = 3 \\ {(A_{0} A_{4})}^{2} = {(A_{0} A_{2})}^{2} = 3 \end{aligned}$
So $(A_{0} A_{1}) (A_{0} A_{2}) (A_{0} A_{4}) = \sqrt{1 \times 3 \times 3} = 3$
Fig. 16.16

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App