+13 A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point P on the edge of the table (as shown below) has a distance of 8 from one wall, and a distance of 9 from the other wall. Find the radius of the table.
+318 Let's visualize the problem:
Imagine a right-angled corner of a room. Place a circular table in this corner so that one edge of the table touches both walls.
Point P: A point on the edge of the table that is 8 units away from one wall and 9 units away from the other.
Radius: The distance from the center of the table to any point on its edge (like point P).
Solution:
Form a right triangle:
The distance from point P to the first wall (8 units) is one leg of a right triangle.
The distance from point P to the second wall (9 units) is the other leg of the right triangle.
The hypotenuse of this right triangle is the diameter of the table, which is twice the radius.
Use the Pythagorean theorem:
a² + b² = c²
8² + 9² = c²
64 + 81 = c²
145 = c²
c = √145
Find the radius:
Since the diameter is twice the radius, the radius is half of √145.
Radius = (√145) / 2
Therefore, the radius of the table is (√145) / 2 units.
