Question

Two concentric circles are of radii 5cm and 3cm.Find length of chord of larger circle which touches the smaller circle.
answer with figure.​

Answer 1

Check the attachment:

Given, OA = OB = 5cm

OM = 3cm

let the chord AB of bigger circle touches the point M of smaller circle

We know that, tangents are perpendicular to the radius of the circle

<OMA = <OMB (each 90°)

In ∆OMA:

AM² = OA² - OM² {By Pythagoras theorem}

=> AM = $\sqrt{(5)^2 - (3)^2}$

=> AM = $\sqrt{25 - 9}$

=> AM = $\sqrt{16}$

=> AM = 4cm

Similarly in ∆OBM, BM = 4cm

So, Length of the chord AB = AM + BM

AB = 4cm + 4cm = 8cm