Question 49

AB is a chord of a circle. The length of AB is 24 cm. P is the midpoint of AB. Perpendiculars from P on either side of the chord meets the circle at M and N respectively. If PM < PN and PM = 8 cm. then what will be the length of PN?

Solution

Share

Let us draw the diagram using the given conditions.


AB = 24 cm and P is the mid-point of AB. Therefore, AP=PB=12 cm. 
MN is perpendicular to AB and passes through P. 
PM < PN. Therefore, M should be closer to A and B than N.
MN and AB are 2 perpendicular chords intersecting at P. 
Therefore, according to the intersecting chords theorem, AP*PB = PM*PN
12*12=8*PN
=> PN = 18 cm.
Therefore, option B is the right answer. 

Get AI Help

Video Solution

video
View More Questions From Geometry

Create a FREE account and get:

  • All Quant Formulas and shortcuts PDF
  • 15 XAT previous papers with solutions PDF
  • XAT Trial Classes for FREE

XAT Quant Questions | XAT Quantitative Ability

XAT Venn Diagrams QuestionsXAT Logarithms, Surds and Indices QuestionsXAT Inequalities QuestionsXAT Geometry QuestionsXAT Profit and Loss Questions

XAT DILR Questions | LRDI Questions For XAT

XAT Quant Based DI QuestionsXAT Quant Based LR QuestionsXAT Data change over a period QuestionsXAT Puzzles QuestionsXAT Selection With Condition Questions

XAT Verbal Ability Questions | VARC Questions For XAT

XAT Para Jumbles QuestionsXAT Miscellaneous QuestionsXAT Grammar and Sentence Correction QuestionsXAT Reading Comprehension QuestionsXAT Critical Reasoning Questions

Free XAT Quant Questions

XAT Logarithms, Surds and IndicesXAT Progressions and SeriesXAT Number SystemsXAT InequalitiesXAT Functions, Graphs and StatisticsXAT Venn DiagramsXAT Linear EquationsXAT Time, Speed and DistanceXAT Averages, Ratio and ProportionXAT Profit and LossXAT GeometryXAT Quadratic EquationsXAT Data SufficiencyXAT Probability, Combinatorics

Related Formulas With Tests

Circle theorems

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