Combination Based on Geometry

A 1, A 2, …, ...

Question

$A_{1}, A_{2}, . . ., A_{18}$ are the vertices of a $18$ sided regular polygon. " $B$ " is an external point such that $A_{1} A_{2} B$ is an equilateral triangle. If $A_{18} A_{1}$ and $A_{1} B$ are the adjacent sides of another regular polygon of $n$ sides, then the value of $n$ is

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

9

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

12

No worries! We‘ve got your back. Try BYJU‘S free classes today!

14

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $9$

$2 π = ∠ A_{18} A_{1} A_{2} + ∠ A_{2} A_{1} B + ∠ A_{18} A_{1} B$
$= \frac{8 π}{9} + \frac{π}{3} + (1 - \frac{2}{n}) π$
$\Rightarrow n = 9$

Suggest Corrections

Similar questions

A_{1}, A_{2}, . . . . A_{n}

n -

\frac{1}{A_{1} A_{2}} = \frac{1}{A_{1} A_{3}} + \frac{1}{A_{1} A_{4}}

n

A_{1}, A_{2}, A_{3} . . . A_{n}

n

| O A_{1} | = 1

| A_{1} A_{2} | | A_{1} A_{3} | . . . . | A_{1} A_{n} | = n

A_{1}, A_{2} . . . . . . . . A_{n}

n

O

n - 1 \sum i = 1 (\to O A_{i} \times \to O A_{i + 1}) =

A_{1}, A_{2}, . . . ., A_{n}

\frac{1}{A_{1} A_{2}} = \frac{1}{A_{1} A_{3}} + \frac{1}{A_{1} A_{4}}

A_{1} A_{2} A_{3} . . . A_{n}

n

\frac{1}{A_{1} A_{2}} = \frac{1}{A_{1} A_{3}} + \frac{1}{A_{1} A_{4}},

Join BYJU'S Learning Program

Select...