Similarly, LD> 2B.In theand LD of quadrilateralPLE 7adjoining figure,

1.	Similarly, LD> 2B.In theand LD of quadrilateralPLE 7adjoining figure, the bisectors ofa guadrilateral ABCD meet CDand AB produced at P and Q respectivelyProve that2
Answer» InΔPBC we have,angle p +pbc+c=180p+1/2 B+C=180⇒eq 1 InΔqad we have Q+A+ADQ=180Q+A+1/2 D=180⇒eq 2 Adding 1 and 2P+Q+A+C+1/2 B+1/2 A=360 But,A+B+C+D=360P+Q+A+C+1/2(B +D)=A+B+C+D P+Q=1/2 (B+D)P+Q=1/2(ABC+ADC)

Similarly, LD> 2B.In theand LD of quadrilateralPLE 7adjoining figure, the bisectors ofa guadrilateral ABCD meet CDand AB produced at P and Q respectivelyProve that2

Answer»

InΔPBC we have,angle p +pbc+c=180p+1/2 B+C=180⇒eq 1

InΔqad we have

Q+A+ADQ=180Q+A+1/2 D=180⇒eq 2

Adding 1 and 2P+Q+A+C+1/2 B+1/2 A=360

But,A+B+C+D=360P+Q+A+C+1/2(B +D)=A+B+C+D

P+Q=1/2 (B+D)P+Q=1/2(ABC+ADC)