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

Question

BigorU [14]

4 years ago

11

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

Mathematics

1 answer:

Vsevolod [243] · Answer 1 · 2021-12-01T15:42:31+03:00

Answer:

AP = RA = 1.5 cm

PB = BQ = 8.5 cm

QC = CR = 3.5 cm

Step-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 = 12

We can substitute the above expressions involving x to find what x is.

(10 -x) +(5 -x) = 12

15 -2x = 12

x = (15 -12)/2 = 1.5

This tells us ...

AP = RA = 1.5 cm

PB = BQ = 8.5 cm

QC = CR = 3.5 cm