TWO CIRCLES OF RADII 10CM AND 8CM INTERSECT AND THE LENGTH OF THE COMMON CHORD IS 12CM.THEN THE DISTANCE BETWEEN THEIR CENTRES IS OPTION 1)8 2)10 3)15 4)13.3

Question

COMPETITIVE EXAM GENERAL QUESTION

Answer 1

Draw the two intersecting circles and label as follows:

 

Circle O with radius 8;  circle P with radius 10

 

AB is chord of intersection and has length = 12

 

I is point on the chord where the radii of the two cirlcles

  will meet

 

Radius drawn perpendicular to a chord will bisect the chord

 

You now have four right triangles formed by the radii of each

circle with the perpendicular drawn from each center point

to the chord of intersection,  we will use one triangle from

each circle

 

OB = 8, BI = 6, find OI by Pythagorean Theorem

 

      BI²  +  OI²  =  OB²               

 

       36  +  OI²  =  64

 

                 OI²   =  √ 28

 

                 OI    =  5.292

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BP = 10,  BI = 6, find PI

 

This is a 3 - 4- 5 right triangle: 6, PI = 8, 10

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Therefor the distance between the centers:

 

   PO = OI + BI

 

   PO = 5.292 + 8

 

   PO = 13.292  ;  Your answer would be : 4

Answer 2

Draw and label a diagram.

Draw a radius from the center of each circle to both ends of the chord.

See the four right triangles?

Use Pythagoras.