MATH SOLVE

4 months ago

Q:
# The sides AB , BC , and AC of a △ABC are tangent to a circle at points P, Q, and R respectively. Find AP, PB, BQ, QC, CR, and RA if AB = 10 cm, BC = 12 cm, and CA = 5 cm. Really need an answer

Accepted Solution

A:

Answer: AP = RA = 1.5 cm PB = BQ = 8.5 cm QC = CR = 3.5 cmStep-by-step explanation:The distance from the vertex to the two nearest tangent points is the same. If we say the distance AP = RA = x, then PB = BQ = 10-x, and QC = CR = 5 -x.Since we know BQ +QC = 12We can substitute the above expressions involving x to find what x is. (10 -x) +(5 -x) = 12 15 -2x = 12 x = (15 -12)/2 = 1.5This tells us ... AP = RA = 1.5 cm PB = BQ = 8.5 cm QC = CR = 3.5 cm