In the given figure, O is the centre of the circle and PQ & PR are the tangents to the circle such that OQ = 8 cm and OP = 17 cm, then the length of the tangent PQ is :
Show Hint
This problem uses the well-known Pythagorean triplet \((8, 15, 17)\).
If you memorize basic triplets like \((3,4,5)\), \((5,12,13)\), and \((8,15,17)\), you can write down the answer of such geometry questions instantly without calculations.
Step 1: Spot the numbers as part of a familiar triple. Before doing any calculation, notice that 8 and 17 are two members of the well known 8-15-17 Pythagorean triple. This suggests the missing side is likely 15. Step 2: Confirm using the tangent-radius right angle. Since the tangent PQ is perpendicular to the radius OQ at the point of contact, triangle OQP is right angled at Q, with OP as the hypotenuse. So the sides must satisfy $OQ^2 + PQ^2 = OP^2$. Step 3: Check the triple against the given values. With $OQ = 8$ and $OP = 17$, this is exactly the 8-15-17 triple, since $8^2 + 15^2 = 64 + 225 = 289 = 17^2$. Step 4: State the tangent length. So PQ must be 15 cm, matching what the Pythagoras calculation confirms.
\[ \boxed{15 \text{ cm}} \]
