Question : Let $ ext{AX}\perp ext{BC}$ of an equilateral triangle $ ext{ABC}$. Then the sum of the perpendicular distances of the sides of $ riangle ext{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 $AX$

Question

Question : Let $ ext{AX}\perp ext{BC}$ of an equilateral triangle $ ext{ABC}$. Then the sum of the perpendicular distances of the sides of $ riangle ext{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 $AX$

Team Careers360 · Accepted Answer

Correct Answer: Equal to $AX$

Solution :
Given: $ ext{AX}\perp ext{BC}$ of an equilateral triangle $ ext{ABC}$.
Let $ ext{O}$ be a point inside the triangle.
Such that $ ext{OD} \perp ext{BC}$, $ ext{OE} \perp ext{AC}$ and $ ext{OF} \perp ext{AB}$.
Since $ ext{ABC}$ is an equilateral triangle.
Such that $ ext{AB = BC = CA}$.
Area of $ riangle ext{ABC}$ = Area of $ riangle ext{OAB}$ + Area of $ riangle ext{OBC}$ + Area of $ riangle ext{OAC}$,
$⇒\frac{1}{2} imes BC imes AX=\frac{1}{2} imes AB imes OF + \frac{1}{2} imes BC imes OD + \frac{1}{2} imes AC imes OE$
$⇒ ext{AX = OF + OD + OE}$ [$\because ext{AB = BC = CA}$]
Hence, the correct answer is 'Equal to $AX$'.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Online Courses

Products

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Student Visas

Exams

Top Schools

Products & Resources

NCERT Study Material

Question : Let AX⊥BC of an equilateral triangle ABC. Then the sum of the perpendicular distances of the sides of △ABC from any point inside the triangle is:Option 1: Equal to BCOption 2: Equal to AXOption 3: Less than AXOption 4: Greater than AX

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CHSL

Download the Careers360 App on your Android phone

Sign In/Sign Up

Question : Let $AX ⊥ BC$ of an equilateral triangle $ABC$ . Then the sum of the perpendicular distances of the sides of $△ ABC$ from any point inside the triangle is:
Option 1: Equal to $B C$
Option 2: Equal to $A X$
Option 3: Less than $A X$
Option 4: Greater than $A X$