SATHEE: Quantitative Aptitude Ques 24

Quantitative Aptitude Ques 24

Question: AD is perpendicular to the internal bisector of $ \angle ABC $ of $ \Delta ABC. $ DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm) is

Options:

A) 4

B) 8

C) 3

D) 6

Show Answer

Answer:

Correct Answer: D

Solution:

Let AD meet BC at F. $ \angle ADB=\angle BDF=90{}^\circ $ As BD is angle bisector. Let $ \angle DBF=\angle ABD=x $ So, $ \angle BAD=\angle BFD $

$ \therefore $ $ \Delta ABD $ and $ \Delta FBD $ are congruent Now, $ \Delta ADE $ is similar to $ \Delta AFC. $ $ [\because DE\parallel BC] $

$ \therefore $ $ \frac{AE}{AC}=\frac{AD}{AF}=\frac{1}{2} $

$ \Rightarrow $ $ AE=\frac{1}{2}AC=\frac{1}{2}\times 12=6,cm $

Quantitative Aptitude Ques 23

Quantitative Aptitude Ques 25

Bank Preparation

IBPS Office Assistants

IBPS RRB Officers

Bank Courses

Recorded Course for English

Recorded Course for Reasoning

Recorded Course for Mathematics

NCERT Books

Important Resources

Banking Awareness

Financial Awareness

Forum

BETA

© 2025 Copyright SATHEE

Privacy Policy

Powered by Prutor@IITK

sathee@iitk.ac.in

Media coverage of SATHEE

Play Store

App Store

The Ministry of Education has launched the SATHEE initiative in association with IIT Kanpur to provide free guidance for competitive exams. SATHEE offers a range of resources, including reference video lectures, mock tests, and other resources to support your preparation. Please note that participation in the SATHEE program does not guarantee clearing any exam or admission to any institute.