Question

Please solve this question​

Answer 1

Step-by-step explanation:

By angle bisector theorem:

$\frac{AP}{PQ} = \frac{AB}{BQ}....(1) \\ \frac{AP}{PQ} = \frac{AC}{CQ}....(2) \\ from \: (1) \: and \: (2) \\ \frac{AP}{PQ} = \frac{AB}{BQ} = \frac{AC}{CQ} \\ let \: \frac{AP}{PQ} = \frac{AB}{BQ} = \frac{AC}{CQ} = k \\ \therefore k \: = \frac{AB}{BQ} = \frac{AC}{CQ} \: \\ \therefore k \: = \: \frac{AB +AC }{BQ +CQ } ( by \: theorem \: on \: equal \: ratios) \\ \therefore k \: = \: \frac{AB +AC }{BC} \\ \therefore \: \frac{AP}{PQ} =\frac{AB +AC }{BC} \\ thus \: proved$