Final answer:
The mathematical statement 'Any angle inscribed in a semicircle is a right angle' can be symbolically represented as 'I → r', signifying if an angle is inscribed in a semicircle (I), then it is a right angle (r).
Step-by-step explanation:
To translate the mathematical statement 'Any angle inscribed in a semicircle is a right angle' into symbolic form, we start by defining our variables: let 'I' represent the statement 'an angle inscribed in a semicircle,' and 'r' represent 'is a right angle.' The symbolic form of the statement is then expressed as I → r, which reads 'If I, then r' or 'I implies r.' This illustrates that whenever we have an inscribed angle in a semicircle (I), it will necessarily be a right angle (r).
In the context of circle geometry, this statement is related to the theorem that any angle inscribed in a semicircle is a right angle, due to the properties of circles and the relationship between angles and arc lengths. When the radius (r) of a circle is used to create an inscribed angle that intercepts a semicircle, the arc spanned is half of the circle's circumference, leading to an angle of 90 degrees or π/2 radians at the inscribed angle, thereby forming a right angle.