Question

31. If two intersecting chords of a circle make equal angles with the diameter passing through
point of intersection, prove that the chords are equal.
​

Answer 1

Step-by-step explanation:

Given:AB is the diameter of the circle with centre O.AP and AQ are two intersecting chords of the circle such that ∠PAB=∠QAB

Proof:In △AOL and △AOM

∠OLA=∠OMB (each 90

∘

)

OA=OA(common line)

∴∠OAL=∠OAM(∠PAB=∠QAB)

∴△AOL≅△AOM by AAS congruence criterion

⇒OL=OM by CPCT

⇒Chords AP and AQ are equidistant from centre O

⇒AP=AQ(chords which are equidistant from the centre are equal.)