Question

In the figure, two circles of radii 8 and 6 are drawn with their centres 12 units apart. At P, one of the points of intersection of the two circles, a line is drawn in such a way that the chords QP and PR have equal length. Find the value

of PQ² /5​

Answer 1

Answer:

ans is 14 I hope its work okay thank you

Answer 2

Answer:

$\frac{PQ^{2} }{5} =26$

Step-by-step explanation:

Given radii of circles equal to 8 and 6

And the chords QP and PR are equal, therefore let $QP=PR=x$

Extend the line joining the centers of two circles to R and S.

Length of the line from R to the point I is

                                  $6+(12-8)=10$

Diameter of the larger circle is $2r=2X8=16$

Using power of a point theorem to the circle passing through QRS, we get

                        $x . 2x=10.(10+16)$

                  $\implies2x^{2} =260$

                    $\implies x^{2} =130$

Therefore the value of $\frac{PQ^{2} }{5} =\frac{130}{5} =26$