Question

Two circles of radii 10 cm and 8 cm
intersect each other, and the length of
the common chord is 12 cm. Find the
distance between their centres.




note: right answer will be marked
as brainlist.
warning: wrong answer will be reported.




उत्तर देना अनिवार्य है|​

Answer 1

Answer:

13.29 cm

Step-by-step explanation:

Let O and O' be the centers of the circle of radii 10 cm and 8 cm respectively.

Let PQ be their common chord.

We have,

OP = 10 cm

O'P = 8 cm

PQ = 12 cm

$PL=\frac{1}{2}PQ=6cm$  (Perpendicular from the center of the circle to a chord bisects the chord).

In right OLP, we have

OP²= OL² + PL²

In right O'LP we have :

(O'P)² = (PL)² + (O'L)²

∴$O'L=\sqrt {O'P^2 - LP^2}$

         $=\sqrt{(8)^2-(6)^2}$

         $=\sqrt{64-36}$

         $=\sqrt{28} = 5.29$

OO' = 8 + 5.29  = 13.29 cm

Therefore, the distance between the two centers is 13.29 cm.