Join WhatsApp Icon CAT WhatsApp Group
Question 9

In triangle ABC, the internal bisector of $$\angle{A}$$ meets BC at D. If AB = 4, AC = 3 and $$\angle{A}$$ = 60° , then the length of AD is

Solution

Share

By using cosine rule we can find BC = $$\sqrt{13}$$ . By angle bisector theorem we have BA / BD = AC / DC . Also BD + DC = $$\sqrt{13}$$. So by substitution we get we get BD = 4*$$\sqrt{13}$$/7 . Now using cosine rule in triangle ABD taking AD = x, we get

$$x^2 - 4*\sqrt3*x + 16*(36/49) = 0$$. Solving the equation we get x = $$\frac{12\sqrt 3}{7}$$ .

Was this solution helpful?

Get AI Help

Video Solution

video
View More Questions From Geometry

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 41+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Geometry QuestionsCAT Functions, Graphs and Statistics QuestionsCAT Miscellaneous QuestionsCAT Time, Speed and Distance QuestionsCAT Logarithms Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Arrangement QuestionsCAT Scheduling QuestionsCAT Puzzles QuestionsCAT Charts QuestionsCAT DI Miscellaneous Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Odd One Out QuestionsCAT Para Summary QuestionsCAT Grammar and Sentence Correction QuestionsCAT Para Jumbles QuestionsCAT Critical Reasoning Questions

Free CAT Quant Questions

CAT LogarithmsCAT Functions, Graphs and StatisticsCAT Time And WorkCAT Averages, Ratio and ProportionCAT Time Speed DistanceCAT Number SeriesCAT Logarithms, Surds and IndicesCAT Averages Mixtures AlligationsCAT Coordinate GeometryCAT RemaindersCAT Quadratic EquationsCAT Progressions and SeriesCAT Simple Interest Compound InterestCAT MensurationCAT GeometryCAT AlgebraCAT Profit and LossCAT ArithmeticCAT Linear EquationsCAT Profit And LossCAT PercentagesCAT Time, Speed and DistanceCAT AveragesCAT MiscellaneousCAT InequalitiesCAT Probability, CombinatoricsCAT Venn DiagramsCAT Number SystemsCAT Data Sufficiency

Related Formulas With Tests

Trignometry - Geometry Triangles - Theorems in triangles

Book Free CAT Mentorship

Get personalized CAT strategy from a 99%iler

500+ students mentored
CAT mentor

Join CAT 2026 course by 5-Time CAT 100%iler

Start your IIM journey with the right preparation and crack CAT 2026.

Enroll Now
Ask AI