SATHEE: Straight Line and Pair of Straight Lines 1 Question 30

Straight Line and Pair of Straight Lines 1 Question 30

30.

If $A_{0}, A_{1}, A_{2}, A_{3}, A_{4}$ and $A_{5}$ 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

(a) $3 / 4$

(b) $3 \sqrt{3}$

(d) $\frac{3 \sqrt{3}}{2}$

$(1998, 2 M)$

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Answer:

Correct Answer: 30. (c)

Solution:

Now, ${(A_{0} A_{1})}^{2} = (1 - \frac{1}{2})^{2} + (0 - \frac{\sqrt{3}}{2})^{2}$

$\begin{aligned} {(A_{0} A_{2})}^{2} = (1 + \frac{1}{2})^{2} + (0 - \frac{\sqrt{3}}{2})^{2} \\ = (\frac{3}{2})^{2} + (- \frac{\sqrt{3}}{2})^{2} = \frac{9}{4} + \frac{3}{4} = \frac{12}{4} = 3 \\ \Rightarrow A_{0} A_{2} = \sqrt{3} \\ and {(A_{0} A_{4})}^{2} = (1 + \frac{1}{2})^{2} + (0 + \frac{\sqrt{3}}{2})^{2} \\ = (\frac{3}{2})^{2} + (\frac{3}{4}) = \frac{9}{4} + \frac{3}{4} = \frac{12}{4} = 3 \\ \Rightarrow A_{0} A_{4} = \sqrt{3} \\ Thus, (A_{0} A_{1}) (A_{0} A_{2}) (A_{0} A_{4}) = 3 \end{aligned}$

Straight Line and Pair of Straight Lines 1 Question 30

30.

Answer:

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Straight Line and Pair of Straight Lines 1 Question 30

30.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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