Q41 of 141 Page 447

In the given figure, A and B are the centers of two circles having radii 5 cm and 3 cm respectively and intersecting at points P and Q respectively. If AB = 4 cm, then the length of common chord PQ is

Given: two circles having radii 6 cm and 3 cm


Construction: join AP


Consider ΔABP


Here,


AP2 = AB2 + BP2


52 = 42 + 32


25 = 16 + 9


25 = 25


∴ ΔABP is right angled triangle


PQ = 2×BP


PQ = 2×3 = 6cm


∴PQ = 6cm

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Three statements are given below:

I. If a diameter of a circle bisects each of the two chords of a circle, then the chords are parallel.


II. Two circles of radii 10 cm and 17 cm intersect each other and the length of the common chord is 16 cm. Then, the distance between their centres is 23 cm.


III. ∠ is the line intersecting two concentric circles with centre O at points A, B, C and D as shown. Then, AC = DB.


Which is true?