In the given figure, P is a point on AB such that AP : PB = 4 : 3. PQ is parallel to AC.
(i) Calculate the ratio PQ : AC, giving reason for your answer. (ii) In triangle ARC, ∠ ARC = 90∘ and in triangle PQS, ∠ PSQ = 90∘. Given QS = 6 cm, calculate the length of AR.
(i) Given, AP: PB = 4: 3.
Since, PQ || AC. Using Basic Proportionality theorem,
Now, PQB =
ACB (Corresponding angles)
QPB =
CAB (Corresponding angles)
(ii) ARC =
QSP = 90o
ACR =
SPQ (Alternate angles)