Question

AB is a chord of circle of radius 4.3cm and P is a point on AB which divides it into two parts in the ratio 7:10. If P is 2.7cm away from the centre o find the length of the AB

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Hence the length of the AB is 6.8 cm.

Step-by-step explanation:

Given:  

Here AB is a chord of circle of radius 4.3 cm and P is a point on AB which divides it into two parts in the ratio 7:10.

As shown in the figure, let AP=7x, PB=10x, OP=2.7 cm, OA= 4.3 cm

Now chord is bisected by perpendicular from the center so,

⇒AM=MB

=$\frac{17x}{2}$  

=8.5x

Also, AM=AP+PM

PM=AM-AP

PM=8.5x−7x

=1.5x

Now in right angle triangle AOM,

$OM^2=4.3^2-(8.5x)^2$

and in right angle triangle OPM,

PM=8.5x−7x=1.5x

$OM^2=2.7^2-(1.5x)^2$

Equating both we get,

$4.3^2-(8.5x)^2=2.7^2-(1.5x)^2$

$(8.5x)^2-(1.5x)^2=4.3^2-2.7^2$

$72.25x^2-2.25x^2=18.49-7.29$

$70x^2=11.2$

$x^2=\frac{11.2}{70}$

$x^2=0.16$

$x=\sqrt{0.16}$

x=0.4

So,

AB=17x

    =17(0.4)

    =6.8 cm

Hence the length of the AB is 6.8 cm.