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Question

The circumference of a ΔABC is O. prove that OBC+BAC=90.
1536666_09486df8f3f1473ea5be6e844c3d038f.png

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Solution

ABC is a triangle and O is the circumcentre.

Refer image,

Draw ODBC, Join OB and OC
In right ΔOBD and right ΔOCD, we have,

hyp. OB=hyp.OC

[Radii of the same circle]

OD=OD

[Common side]

ΔOBDΔOCD [By RHS cong. Role]

1=2 and 3=4 [By C.P.C.T]

Now, BOC=21 and BOC=2A

21=2A1=A

A=2......(1) [1=2]

A+4=2+4 [Adding 4 to both sides]

A+3=900[2 +4=900and4=3]

BOC=A=900

Hence, proved.

1820615_1536666_ans_efb538785f354ffc94d4707d820f6d2c.png

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