Identical 8831

In the triangle ABC, the point P lies closer to point A in the third of the line AB, the point R is closer to the point P in the third of the line P, and the point Q lies on the line BC so that the angles P CB and RQB are identical.

Determine the ratio of the area of the triangles ABC and PQC.

Correct answer:

p =  9:2

Step-by-step explanation:

AB = a AP = 31 a PR= 31   32 a = 92 a RB= (1  31  92) a = 94 a  S(ABC) = 2a h  S(APC) = 2AP h = 231  a h = 31   S(ABC) S(PCB) = S(ABC)  S(APC) = 32   S(ABC)  PCB  RQB   h2 = 32   h S(PQB) = 2PB h2 = 232 a 32 h = 94   S(ABC)  S(PQC) = S(ABC)  S(APC)  S(PQB) = S(ABC)( 1  31  94) S(PQC) = k   S(ABC)  k=13194=920.2222 p =  S(ABC) : S(PQC) p=1/k=1/92=1:92=1 29=21 9=29=421=4.5=9:2

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