Question

12. 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

Step-by-step explanation:

R.E.F image

AP=PB⇒ 'P' is mid pt

AB=2PB

PB

2

+OP

2

=13

2

(In ΔOPB)

OP

2

=

(7−3)

2

+(9−6)

2

=

4

2

+3

2

=5

∴PB

2

=

13

2

−5

2

=12

⇒

AB=24unit

solution

Answer 2

Answer:

24 units

Step-by-step explanation:

Let the centre be O(3,6),

P(7,9) is the midpoint of the chord.

According to property of the Circle , if we draw a line from the centre to the mid point of a chord , it will pe perpendicular to the chord.

OP will be perpendicular to Chord APB,

Length of OP will be = square root { ( 7-3)^2 + (9-6)^2}

OP= square root (25)

OP = 5 units

Now OPA will make a triangle in which angle OPA will be 90 degree, OA will be 13 units, OP will be 5 units and by using Pythagoras theorem we can find AP

AP^2 = OA^2- OP^2

AP^2 = 144

AP = 12 units

we know from the question that AB = 2AP since P is the midpoint of AB

therefore AB= 24 units