Question

. If no equal chords of a cinle
intersect within the circle, prove that the segments of
one chord are equal to corresponding segments of the
other chord.​

Answer 1

AB = PQ ...(1)

draw ON & OM perpendicular to AB & PQ

AN = BN & PMQM

To prove:- seg. AB = seg. PQ

Proof:- In ∆ONS & ∆OMS

OS = OS (Common side)

ON = OM ( each chord of a circle are equidistant from a center)

angle ONS = angle OMS = 90°

∆ONS congruent to ∆OMS (SAS test)

SN = SM (cpct)

Now, AN = PM....(2)

Also, SN = SM .......(3)

add (2)&(3)

AN+SN = PM+SM

AS = PS........(4)

Now, subtract (1)&(4)

AB-AS = PQ-PS

BS = QS.....(5)

From (4)&(5)

Seg. AB = Seg. PQ

it took so much time dud.......✌✌✌✔