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=31a PR=31 32a=92a RB=(13192)a=94a  S(ABC)=2a h  S(APC)=2AP h=231 a h=31 S(ABC) S(PCB)=S(ABC)S(APC)=32 S(ABC)  PCBRQB  h2=32 h S(PQB)=2PB h2=232 a 32 h=94 S(ABC)  S(PQC)=S(ABC)S(APC)S(PQB)=S(ABC)(13194) 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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