(i) In
ΔABC and
ΔAMP∠ABC=∠AMP (Both are equal to 90˚)
∠BAC=∠PAM (Common Angles)
∠APM=∠ACB (Common Angles)
Therefore
By AAA corollary, ΔABC∼ΔAMP
(ii) Now,
AP=15 cm,PM=12 cm
Using Pythagoras theorem in ΔAPM, we get
AM=√AP2−PM2
AM=√225−144=9 cm
ABBP=AMMC
105=9MC
⇒MC=4.5 cm
Also,
ABBC=AMMP
10BC=912
⇒BC=1209 cm
AB=10 cm
![625194_578417_ans.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/625194_578417_ans.png)