Question

In the figure, PQ ll BC, PR ll BQ, Prove: AQ^2= AR x AC

Answer 1

Answer:

Explanation:

In Δ ABQ,

PR║BQ

∴ By  BPT

$\frac{AR}{AQ} = \frac{AP}{AB}$             -- 1

Similarly, In Δ ABC,

PQ║BC

∴ By BPT,

$\frac{AP}{AB} = \frac{AQ}{AC}$           -- 2

∴ By equating 1 and 2,

$\frac{AR}{AQ} = \frac{AQ}{AC}\\\\AQ^{2} = AR .AC$

Hence Proved.