Question

△ABC,AP⊥BC,BQ⊥AC, B−P−C,A−Q−C then prove that, △CPA∼△CQB. 4M IfAP=7, BQ=8, BC=12 then find AC.​

Answer 1

Answer:

To prove:△CPA≅△CQB

Proof:In △CPA and △CQB

∠CPA=∠CQB=90

∘

(given)

∠C=∠C (common)

By AA similarity criterion,

△CPA≅△CQB

Hence proved.

Now,

BQ

AP

=

BC

AC

since corresponding sides are proportional.

⇒AC=

BQ

AP

×BC

=

8

7

×12=10.5