Draw a circle with centre $O$ and radius $6$ cm. Take a point $P$ outside the circle at a distance of $10$ cm from $O$. Draw tangents to the circle from point $P$. Let the tangents intersect the circle in points $A$ and $B$. Find $BP$.

Because the tangent to a circle is perpendicular to the radius at the point of contact, triangle OBP forms a right angled triangle with the right angle at B. In this triangle, the hypotenuse OP is 10 cm, and one leg OB (the radius) is 6 cm. Applying the Pythagorean theorem, the square of the other leg BP equals OP squared minus OB squared. This gives BP squared as 100 minus 36, which equals 64. Taking the square root of 64 yields the length of BP as 8 cm.

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