CAT Practice : Mensuration

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Very often mensuration questions are just an extension of geometry. If your Geometry fundaes are good, Mensuration is a walk in the park.

Circles and Chords

Q.3: Two mutually perpendicular chords AB and CD meet at a point P inside the circle such that AP = 6 cms, PB = 4 units and DP = 3 units. What is the area of the circle?
1. ${125{\pi} \over 4}$ sq cms
2. ${100{\pi} \over 7}$ sq cms
3. ${125{\pi} \over 8}$ sq cms
4. ${52{\pi} \over 3}$ sq cms

Choice A. ${125{\pi} \over 4}$ sq cms

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Detailed Solution

As AB and CD are two chords that intersect at O, AP × PB = CP × PD
6 × 4 = CP × 3
CP = 8
From center O draw OM ⊥r AB and ON ⊥r CD.
From the center a line ⊥r to a chord bisects the chord.

So, we have AM = MB = 5 cm
MP = 1 cm, ON = 1 cm, CD = 11 cm, CN = 5.5 cm
ON2 + CN2 = OC2
12 + 5.52 + r2
1 + 30.25 = r2

Area = πr2
π × 31.25
31.25π = ${125{\pi} \over 4}$ sq cms

Correct Answer: ${125{\pi} \over 4}$ sq cms

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More questions from Mensuration

Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.