(2) In AABC, A-P-B and A-Q-C such thatparts whose areas are equal. Find the valtue ofseg PQ ll side BC and seg PQ divides AABC in twoBPAB

(2) In AABC, A-P-B and A-Q-C such thatparts whose areas are equal. Fin

1.	(2) In AABC, A-P-B and A-Q-C such thatparts whose areas are equal. Find the valtue ofseg PQ ll side BC and seg PQ divides AABC in twoBPAB
Answer» Solution:-Given : PQ is parallel to BC and PQ divides triangle ABC into two parts.To find : BP/ABProof : InΔ APQΔ ABC,∠ APQ =∠ ABC (As PQ is parallel to BC)∠ PAQ =∠ BAC (Common angles)⇒Δ APQ ~Δ ABC (BY AA similarity)Therefore,ar(Δ APQ)/ar(Δ ABC) = AP²/AB²⇒ ar(Δ APQ)/2ar(Δ APQ) = AP²/AB²⇒ 1/2 = AP²/AB²⇒ AP/AB = 1/√2⇒ (AB - BP)/AB = 1/√2⇒ AB/AB - BP/AB = 1/√2⇒ 1 - BP/AB = 1/√2⇒ BP/AB = 1 - 1/√2⇒ BP/AB =√2 - 1/√2