Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA congruent to Arc PYB.

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.

Answers (1)

Given that the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q

Let AB be the chord having centre at O.

Let PQ be the perpendicular bisector of the chord AB, which intersects AB at M and it is passes through the centre O.

Join AP and BP

In \triangle APM and \triangle BPM

AM = MB (PM is the perpendicular bisector of AB)

PM = PM (Common)

\angle PMA = \angle PMB  (90° each)

\therefore \triangle APM \cong \triangle BPM (SAS congruence)

PA = PB  (by CPCT)

If 2 chords of a circle are equal, then corresponding arcs are congruent

Hence, arc PXA \cong  arc PYB.

Hence proved

Posted by

infoexpert24

View full answer

Similar Questions

Latest Question