Question

prove:suppose two chords of a circle intersect each other in the interior of the circle then the products of the lenghts of the two segment of one chord is equal to the product of the lenght of the two segment of the other chord​

Answer 1

products of the lengths of the two segment of one chord is equal to the product of the length of the two segment of the other chord​

Step-by-step explanation:

Let say AB & CD are two chords intersecting at AP

we need to show that

AP * BP = CP * DP

Angle formed by chord AD

∠ABD = ∠ACD

=> ∠PBD = ∠ACP

    ∠DPB   = ∠APC

=>  Δ DPB ≈ ΔAPC

=> DP/AP  = PB/PC  = DB/AC

=> DP/AP   = BP/CP

=> CP * DP = AP * BP

=> AP * BP = CP * DP

QED

Proved

products of the lengths of the two segment of one chord is equal to the product of the length of the two segment of the other chord​

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