1. If V1 , V2 (V2 > V1) be the diameters of two concentric circles and Z be the length of a chord of a circle which is tangent to the other circle, prove that :
Let XY be a chord of a circle which touches the other circle at Z. Then
∴ By Pythagoras Theorem,
2. Two tangents AB and AC are drawn from an external point to a circle with centre 0. Prove that BOCA is a cyclic quadrilateral.
Sol. We know that, tangents to a circle is perpendicular to its radius at the point of contact.
Sum of opposite angles of quadrilateral BOCA is
Hence, BOCA is a cyclic quadrilateral.