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
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
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 $AX$'.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : In $\triangle ABC$, AB = BC = $k$, AC =$\sqrt2k$, then $\triangle ABC$ is a:
Question : $\triangle ABC$ is an equilateral triangle. The side $BC$ is produced to point $D$. If $A$ joines $D$ and $B C=CD$, then the degree measure of angle $CAD$ is equal to:
Question : The sides of similar triangle $\triangle ABC$ and $\triangle DEF$ are in the ratio of $\frac{\sqrt{3}}{\sqrt{5}}$. If the area of $\triangle ABC$ is $90 \text{ cm}^2$, then the area of $\triangle DFF\left(\right.$ in $\left.\text{cm}^2\right)$ is:
Question : In $\triangle$ABC, BD and CE are perpendicular to AC and AB respectively. If BD = CE, then $\triangle$ABC is:
Question : A triangle $\text{PQR}$ has three sides equal in measurement and if $\text{PM}$ is perpendicular to $\text{QR}$, then which of the following equality holds?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile