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

R.E.F image

$AP=PB\Rightarrow$ 'P' is mid pt

$AB=2PB$

$P{B}^2+O{P}^2={13}^2$ (In $\Delta OPB)$

$O{P}^2=\sqrt{(7-3{)}^2+(9-6{)}^2}=\sqrt{4^2+3^2}=5$

$\therefore P{B}^2=\sqrt{{13}^2-5^2}=12$

$\Rightarrow AB=24unit$