Equation of line in Straight lines

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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

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Equation of line in Straight lines

Remember concepts with our Masterclasses.

Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit radius then the product of the lengths of the line segments A0A1,A0A2 and A0A4is

The vertices of the hexagon be as shown inthe figure A0A12=14+34=1A0A22=94+34=3A0A42=A0A22=3So A0A1A0A2A0A4=1×3×3=3 Fig. 16.16

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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