Question : Let $\text{AX}\perp \text{BC}$ of an equilateral triangle $\text{ABC}$. Then the sum of the perpendicular distances of the sides of $\triangle \text{ABC}$ from any point inside the triangle is:
Option 1: Equal to $BC$
Option 2: Equal to $AX$
Option 3: Less than $AX$
Option 4: Greater than $AX$
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: Equal to $AX$
Solution :
Given: $\text{AX}\perp \text{BC}$ of an equilateral triangle $\text{ABC}$.
Let $\text{O}$ be a point inside the triangle.
Such that $\text{OD} \perp \text{BC}$, $\text{OE} \perp \text{AC}$ and $\text{OF} \perp \text{AB}$.
Since $\text{ABC}$ is an equilateral triangle.
Such that $\text{AB = BC = CA}$.
Area of $\triangle \text{ABC}$ = Area of $\triangle \text{OAB}$ + Area of $\triangle \text{OBC}$ + Area of $\triangle \text{OAC}$,
$⇒\frac{1}{2} \times BC \times AX=\frac{1}{2} \times AB \times OF + \frac{1}{2} \times BC \times OD + \frac{1}{2} \times AC \times OE$
$⇒\text{AX = OF + OD + OE}$ [$\because\text{AB = BC = CA}$]
Hence, the correct answer is 'Equal to $AX$'.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
