Question

is the circumference of the triangle ABC and OD is perpendicular on BC prove that angle b o d is equal to angle A

Answer 1

Hope that this answer will help you

Answer 2

AnswEr:

$\bf{Solution:-}$

Join OB and OC.

In ∆OBD and OCD, we have

1. OB = OC [Each equal to the radius of circumcircle ]
2. $\angle$ODB = ODC [Each equal to 90° ]
3. OD = OD. [ Common ]

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$\therefore$ ∆OBD $\cong$ OCD

$\implies$ $\angle$ BOD = $\angle$ COD

$\implies$ $\angle$BOC = 2$\angle$BOD = 2$\angle$COD.

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Now, arc BC subtends $\angle$BOC at the centre and $\angle$BAC = $\angle$A at a point in the remaining part of the circle.

$\therefore$ BOC = 2 $\angle$A

$\Rightarrow$ 2 $\angle$BOD = 2 $\angle$A

$\Rightarrow$ $\angle$ BOD = $\angle$ A

#BAL

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