2 Views

Question : The sides AB, BC, and AC of a $\triangle {ABC}$ are 12 cm, 8 cm, and 10 cm respectively. A circle is inscribed in the triangle touching AB, BC, and AC at D, E, and F respectively. The difference between the lengths of AD and CE is:

Option 1: 4 cm

Option 2: 5 cm

Option 3: 3 cm

Option 4: 2 cm


Team Careers360 5th Jan, 2024
Answer (1)
Team Careers360 23rd Jan, 2024

Correct Answer: 4 cm


Solution :
Given: The sides AB, BC, and AC of a $\triangle {ABC}$ are 12 cm, 8 cm, and 10 cm respectively.
Tangents from a fixed point outside the circle always have the same length.
⇒ AD = AF, FC = CE, and BE = BD
Let the AD and CE be $x$ and $z$ respectively.
⇒ BE = BD = 12 - $x$
Also, CE = BC – BE
⇒ $z=8-12+x$
⇒ $x-z=4$
⇒ AD – CE = 4 cm
So, the difference between the lengths of AD and CE is 4 cm.
Hence, the correct answer is 4 cm.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books