Question

Please give me answer it was very helpful to me ​

Answer 1

GIVEN:

• OD is the bisector of ∠BOC
• OD ⊥ OE

TO FIND:

• Show that the points A, O and B are collinear.

SOLUTION:

Since OD and OE are the bisectors of ∠AOC and ∠BOC respectively.

$\rm{\therefore \angle AOD = \angle COD }$

and,

$\rm{ \angle BOE = \angle COE }$

Also,

$\rm{ \angle DOE = 90\degree}$

Now,

$\rm{ \angle AOC + \angle BOC = \angle AOD + \angle COD + \angle BOE + \angle COE }$

$\rm{\dashrightarrow \angle COD + \angle COD + \angle COE + \angle COE }$

$\rm{\dashrightarrow \angle AOC + \angle BOC = 2 \angle COD + 2 \angle COE}$

$\rm{\dashrightarrow 2 (\angle COD + \angle COE)}$

$\rm{\dashrightarrow 2 \angle DOE }$

$\rm{\dashrightarrow 2 \times 90\degree= 180\degree}$

❝ Hence, points A, O and B are collinear ❞

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