Question

एबीसी 80 पॉइंट्स ऑन अ सर्कल प्रूफ द परपेंडिकुलर बाईसेक्टर ऑफ ए बीबीसी एनसीएआर कॉन्करेंट ​

Answer 1

Answer:

ANSWER

In △POX and △QOX

OP=OQ radius of circle C

1

XP=XQ radius of circle C

2

OX=OX(common)

∴△POX≅△QOX by SSS congruence rule

∠POX=∠QOX by C.P.C.T ..(1)

Also, In △POR and △QOR

OP=OQ radius of circle C

1

∠POR=∠QOR since ∠POX=∠QOX

OR=OR (common)

∴△OPX≅△OQX by SAS congruence rule

PR=QR by CPCT

and ∠PRO=∠QRO by CPCT ....(2)

Since PQ is a line

∠PRO+∠QRO=180

∘

(linear pair)

∠PRO+∠PRO=180

∘

from (2)

⇒2∠PRO=180

∘

⇒∠PRO=

2

180

∘

=90

∘

∴∠QRO=∠PRO=90

∘

Also, ∠PRX=∠QRO=90

∘

(vertically opposite angles)

∠QRX=∠PRO=90

∘

(vertically opposite angles)

Since ∠PRO=∠QRO=∠PRX=∠QRX=90

∘

∴,OX is the perpendicular bisector of PQ

Step-by-step explanation:

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