Answer:
127.5 cm
Step-by-step explanation:
You want the length of the perimeter of the figure of a circle of 19 cm radius with tangents that meet at right angles at point P.
Square
If we designate the points of tangency as A and B, the figure OAPB is a square. Each angle is a right angle, and each side has length equal to the radius of the circle: 19 cm.
The lengths of the two sides AP and BP will total 2·19 cm = 38 cm.
Arc
The long arc AB will be 3/4 of the circumference of the circle:
arc AB = (3/4)(2πr) = 1.5π(19 cm) ≈ 89.5 cm
Belt
The length of the belt that wraps the figure will be the sum of these lengths:
38 cm +89.5 cm = 127.5 cm
The length of the belt is 127.5 cm.
