38 Views

Question : A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm, and AC = 24 cm, and sides AB, BC, and AC touch circle at D, E, and F, respectively. The measure of AD is:

Option 1: 10 cm

Option 2: 20 cm

Option 3: 6 cm

Option 4: 14 cm


Team Careers360 23rd Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: 10 cm


Solution :


Given: A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm, and AC = 24 cm, and sides AB, BC, and AC touch circle at D, E, and F, respectively.
We know that tangents drawn from an external point to a circle are equal in length.
Let AD = AF = a, BD = BE = b and CE = CF = c
According to the question,
AB = a + b
⇒ 16 = a + b .......(1)
BC = b + c
⇒ 20 = b + c .......(2)
AC = a + c
⇒ 24 = a + c .......(3)
Now, On adding equations (1), (2), and (3), we get
⇒ 16 + 20 + 24 = a + b + b + c + a + c
⇒ 60 = 2(a + b + c)
⇒ a + b + c = 30
Now putting the value of (b + c) in the above equation,
⇒ a + 20 = 30
⇒ a = 10 cm
Hence, the correct answer is 10 cm.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

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