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The centre of circumcircle of triangle …

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The centre of circumcircle of triangle of ABC is O .prove that angle OBC +angle BAC =90°

Posted by Rima Paul 8 years, 9 months ago

CBSE > Class 09 > Mathematics

1 answers

Jheel Porwal 8 years, 9 months ago

OB=OC(radii)

Let ang.OBC=ang.OCB=x

In triangle BOC

Ang.OBC + ang. OCB + BOC= 180

x + x +ang.BOC=180

Ang.BOC= 180 - 2x ........ eq. 1

Ang.BOC=2 Ang.BAC [arc BC subtended ang.BOC at the centre & ang.BAC in segment]

Using eq. 1

2 ang.BAC= 180 - 2x (divide by 2 to

Both sides)

2ang.BAC = 180 - 2x

<hr />

2 2 2

Ang.BAC = 90 - x

Ang.BAC = 90 - ang. OBC

Ang.OBC + ang.BAC = 90 degrees.

Hence proved!

0Thank You

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