2- plz draw fig and then solve this

two concentric circle has been drawn with centre o a right angled triangle inside the circle in such a way that hypotenuse touches the smaller circle as a tangent of of smaller circle and perpendicular is drawn as the radius of bigger circle and the base is also the radius of bigger circle find the radius of smaller circle

According to Question,

AB = hypotenuse of the right angled triangle

AB touches the smaller circle (C_{2}) as a tangent and OA = OB = R (radius of bigger circle)

⇒ (AB)² = R² + R² + = 2R²

As AB is a chord of circle C_{1} and O is centre.

So OP ⊥ AB and P will bisect AB

Now, OBD is a right angled triangle

∴ (OP)² = (BO)² – (BP)²

Hence, Radius of smaller circle should by times the radius of bigger circle.

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