Question

If two circles intersect each other at points A and D.If the diameter AB intersect the circle with centre P at point N and diameter AC intersect the circle with center Q at point M.Then prove that ACxAM=AB x AN.​

Answer 1

||✪✪ QUESTION ✪✪||

If two circles intersect each other at points A and D.If the diameter AB intersect the circle with centre P at point N and diameter AC intersect the circle with center Q at point M.Then prove that ACxAM=AB x AN. ?

|| ✰✰ ANSWER ✰✰ ||

❁❁ Refer To Image First .. ❁❁

From image In ΔACN and ΔABM we have :-

→ ∠MAB=∠NAC ( common angle)

→ ∠AMB=∠ANC ( semi circle angle is a right angle)

∴ Δ ACN ≈ Δ ABM (By AA Similarity)

So ,,

→ AC/AB=AN/AM

Cross - Multiplying ,,

→ AC × AM = AB × AN (✪✪ Hence Proved ✪✪)