CAT WhatsApp Group

Question 59

A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of circle to the area of rhombus is

Solution

Let the length of radius be 'r'.

From the above diagram,

$$x^2+r^2=6^2\ $$....(i)

$$\left(10-x\right)^2+r^2=8^2\ $$----(ii)

Subtracting (i) from (ii), we get:

x=3.6 => $$r^2=36-\left(3.6\right)^2$$ ==> $$r^2=36-\left(3.6\right)^2\ =23.04$$.

Area of circle = $$\pi\ r^2=23.04\pi\ $$

Area of rhombus= 1/2*d1*d2=1/2*12*16=96.

.'. Ratio of areas = 23.04$$\pi\ $$/96=$$\frac{6\pi}{25}$$

Get 3 Free CAT Mock Tests with Expert Video Solutions Get 3 Free CAT Mock Tests

video

View More Questions From Geometry

Create a FREE account and get:

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

maruti sir image

CAT Quant Questions | CAT Quantitative Ability

CAT Profit And Loss Questions CAT Venn Diagrams Questions CAT Averages Questions CAT Probability, Combinatorics Questions CAT Arithmetic Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Games and Tournamnents Questions CAT Table based DI Sets Questions CAT Scheduling Questions CAT Data Interpretation Basics Questions CAT 2D & 3D LR Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Vocabulary Questions CAT Grammar and Sentence Correction Questions CAT Critical Reasoning Questions CAT Reading Comprehension Questions CAT Para Summary Questions

Related Formulas With Tests

Quadrilateral - Areas and Properties