CAT 2015 Quantitative Ability

Question : 32 of 34

Marks: +1, -0

ΔABC is a right angled triangle, with ∠B = 90°, AB = 20 cm and BC = 21cm. A circle with centre O is inscribed in triangle ABC. OD, OE and OF are perpendiculars drawn on the sides AB, BC and CA respectively. Find the ratio of the area of the quadrilateral FOEC to the area of the quadrilateral ADOF.

15:14
14 : 15
12 : 11
7:5

Validate

Solution:

AC=

√{AB^2 + BC^2}

= 29cm

and (20 - r)+(21 - r) = 29

or 2r = 41-29

⇒ r=6cm

∆OEC ≡ ∆OFC (RHS)

Area( □FOEC) = 2 × Area (∆OEC) =

2×1/2× 15×6 =90

\text"cm"^2

Similarly ∆AOD ≅ ∆AOF (RHS)
Area( □ADOF) = 2 × Area (∆AOD) = 2×

1/2

×14×6 = 84

\text"cm"^2

{\text"Area(□ FOEC)"} /{\text"Area( □ADOF)"}=90/84 = 15/14

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