Q1. Prove that the lengths of tangents drawn from an external point to a circle are equal.
Q2. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
Q3. A quadrilateral ABCD is drawn to circumscribe a circle. Prove that $AB + CD = AD + BC$.
Q4. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Q5. Let $x$ be tangent from A. Semi-perimeter $s = 14+x. Using Heron's formula and $Area = r \times s, we solve for $x$ to find $AB = 15\text{ cm}, AC = 13\text{ cm}$.
