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NCERT Exemplar Solutions Class 9 Mathematics Solutions for Circles - Exercise 10.3 in Chapter 10 - Circles

Question 2 Circles - Exercise 10.3

If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA ∠ Arc PYB.

Answer:

NCERT Exemplar Solutions - Mathematics - class 9 chapter Circles Question 2 Solution image

According to the question,

We have,

PQ is the perpendicular bisect of AB,

So, we get,

AM = BM …eq.(1)

In △APM and △BPM,

From eq.(1),

AM = BM

∠AMP = ∠BMP = 90o

PM = PM [Common side]

Therefore, △APM ≅ △BPM [By SAS congruence rule]

So, AP = BP [CPCT]

Hence, arc PXA ≅ Arc PYB

Therefore, if two chords of a circle are equal, then their corresponding arcs are congruent.

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