CAT Practice : Coordinate Geometry

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What do you need to find, to calculate the area of a triangle? Determine its base and altitude!

Circles touching externally

    Q.30: Two circles with centres O1 and O2 touch each other externally at a point R. AB is a tangent to both the circles passing through R. P’Q’ is another tangent to the circles touching them at P and Q respectively and also cutting AB at S. PQ measures 6 cm and the point S is at distance of 5 cms and 4 cms from the centres of the circles. What is the area of the triangle SO1O2?
    1. 9 cm2
    2. 3(4 + )/2 cm2
    3. 27/2 cm2
    4. (3)/2 cm2

 

  • Correct Answer
    Choice (B). 3(4 + )/2 cm2

Detailed Solution



From the diagram we see that SP, SR are tangents to circle1 from same point S. Similarly SR, SQ are tangents from same point to circle 2.

SP = SR; SQ = SR implies SP = SQ

Given PQ = 6cm

SP + SQ = 6

Therefor SR = SP = SQ = 3 cm.


SR is the altitude to the triangle SO1O2. We need to find the length of the base O1O22 to determine the area.

O1RS is a right angled triangle with hypotenuse = 5 and one side = 3

Therefore, O1R = = 4 cm

Similarly, O2RS is a right angled triangle with hypotenuse = 4 and one side = 3

Therefore, O2R = = cm

O1O2 = O1R + O2R = 4 +

Area of the triangle SO1O2 = 1/2 * SR * O1O2 = 1/2 * 3 * (4 + ) cm2.



Correct Answer: (B). 3(4 + )/2 cm2



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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.