From a point P which is at a distance of 17 cm from the centre O of a circle of radius 8 cm, the pair of tangents PQ and PR to the circle are drawn. The area of triangle OPQ is :

Step 1: Identify given values and properties

We are given that the distance from point P to the center O is 17 cm, so $OP = 17\text{ cm}$. The radius of the circle is 8 cm, so $OQ = 8\text{ cm}$ (where Q is the point of tangency). A key property of tangents is that the radius drawn to the point of tangency is perpendicular to the tangent. Therefore, $\triangle OPQ$ is a right-angled triangle with the right angle at Q.

Step 2: Calculate the length of the tangent PQ

Since $\triangle OPQ$ is a right-angled triangle at Q, we can use the Pythagorean theorem to find the length of the tangent PQ. The hypotenuse is OP, and OQ is one of the legs. Substituting the given values, we calculate PQ.

Step 3: Calculate the area of triangle OPQ

The area of a right-angled triangle is half the product of its perpendicular sides. In $\triangle OPQ$, OQ and PQ are the perpendicular sides. We substitute their lengths to find the area.

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