Question

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, $\angle$ ARC = ${90}^{\circ }$ and in triangle PQS, $\angle$ PSQ = ${90}^{\circ }$. Given QS = 6 cm, calculate the length of AR.

Answer 1

(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 = 90^o

ACR = SPQ (Alternate angles)