CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

This question is from CAT Mensuration in CAT Geometry. Details about two perpendicular chords are given and we need to find out the area of the circle. Mensuration Questions in the CAT exam can be solved with practical approach and thought process rather than just knowing theorems from CAT Geometry. Even if one is not completely prepared for CAT Geometry exam, he or she should be able to do well in Mensuration problems tested by the CAT Exam. Knowing Mensuration formulas is important. Make sure you master Mensuration questions for CAT exam.

Question 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. 125π/4 sq cms
2. 100π/7 sq cms
3. 125π/8 sq cms
4. 52π/3 sq cms

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Geometry - Mensuration: Very often mensuration questions are just an extension of geometry. If your Geometry fundaes are good, Mensuration is a walk in the park.

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 = 125π/4 sq cms

The question is "What is the area of the circle?"

Hence, the answer is 125π/4 sq cms.

Choice A is the correct answer.