Geometry Practice Test 7

Question : 7 of 28

Marks: +1, -0

Two circles with same radius r intersect each other and one passes through the center of the other. Then the length of the common chord is:

Solution:

OA = r
OP =

r/2

AP = x

By Pythagoras theorem,

(OA)^2

(OP)^2+(AP)^2

(r)^2

(r/2)^2 + (AP)^2

r^2-r^2/4

AP^2

{3r^2}/4

AP^2

AP =

{√3r}/2

Length of the chord AB =

√3r

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