Question

point A ( 5,1 ) is the centre of the circle with radius 13 unit AB. perpendicular chord PQ. B is ( 2, -3 ). The length of chord PQ is​

Answer 1

Answer:

The radius of the circle is 13 cm and AB is chord which is at a distance of 12 cm from the center. Then the length of the chord is

A. 16 cm

B. 10 cm

C. 8 cm

D. 15 cm

Solution(By Examveda Team)

Miscellaneous mcq solution image

P be the mid point of AB, So

AP = PB

OP = 12 cm = distance of chord from center

And

AO = 13 cm = Radius

Now, OPA forms a right angle triangle.

Now, by pythagorous theorem,

AO2 = OP2 + AP2

AP2 = AO2 - OP2

AP2 = 132 - 122

AP2 = 169 - 144

AP2 = 25

AP = 5 cm.

Now,

AB = AP + PB = AP + AP = 5 +5 = 10 cm.

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