Question

in the adjoining figure of circle MN // PQ prove that: chord PB=QB:​

Answer 1

Given :-

• MN || PQ .

To Prove :-

• PB = QB .

Solution :-

from image we can see that,

→ ∠ACP = ∠AQP = Let x° { Equal chords makes equal angle at the circumference .} ------- Eqn.(1)

and,

→ ∠AQP = ∠CNB = x° {since it is given that, MN || PQ , so, corresponding angles are equal .} ------- Eqn.(2)

then, In Quadrilateral AMNC,

→ ∠ACM = ∠MNA = x° { from Eqn.(1) and Eqn.(2) .}

therefore,

→ ∠NCM = ∠MAN = Let y° .

now as we can see that,

→ ∠NCM = y° = Angle made by chord PB on circumference .

→ ∠MAN = y° = Angle made by chord QB on circumference .

since both angles are equal to y° .

we know that, if Equal angles are made at the circumference by two chords , then they are equal in length .

Hence, we can conclude that, Chord PB is equal to chord QB .

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