In a plane, points p and q are 20 inches apart. if point r is randomly chosen from all the points in the plane that are 20 inches from p, what is the probability that r is closer to p than it is to q?
a. 00
b. 1414
c. 1313
d. 1212
e. 23

E.

Step-by-step explanation:

Consider a circle having centre P and radius 20 inches,

So, the area of the circle,

Also, suppose points Q and R are on the circumference,

i.e. PQ = PR = 20 inches,

If QR = 20 inches,

So, triangle PQR is an equilateral triangle,

⇒ m∠RPQ = 60°,

Now, suppose R' is another point on the circle,

Such that, ΔPQR ≅ Δ PQR',

⇒ m∠QPR' = 60°,

Thus, minor angle, m∠RPR' = m∠RPQ + m∠QPR' = 60° + 60° = 120°,

⇒ major angle, m∠RPR' = 360° - 120° = 240°,

So, the area of the circle where a point on the circumference is closer to P than it is to Q

Hence, the probability that a point is closer to P than it is to Q =

i.e. OPTION E is correct.

16 is the absolute value

step-by-step explanation: