Question

The centre of a circle of radius 13 units is the point (3, 6). P(7, 9) is a point inside the circle. APB is a chord of the circle such that AP = PB. Calculate the length of AB.

Answer 1

The length of AB is 24 units.

Explanation:

OA = OB

Let "O" be the center of the circle then

OP = √ (3 - 7)^2 + ( 6 - 9)^2

OP = √ (-4)^2 + ( -3)^2

OP = √ 16 + 9 = √ 25 =5 units

Radius of circle OA = 13 units

≤APO = 90°

AP^2 = AD^2 - OP^2 = (13)^2 - )(5)^2

AP^2  = 169 - 25 = 144

Therefore AP = √144 = 12 units

AB = 2 AP = 2 x 12 = 24 units

Hence the length of AB is 24 units.

Also learn more

In figure AP and bp are tangents to a circle with Centre O such that Ap is equal to 5 cm and angle APB is equal to 60 degree find the length of Chord AB. ?

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