Mathematics

O is any point inside a triangle ABC. The bisector of $\angle AOB$, $\angle BOC$ and $\angle COA$ meet the sides, AB, BC and CA in point D, E and F respectively,therefore,$AD\times BE$ = $DB\times FA$

False

SOLUTION
Given: $\triangle ABC$, CX is bisector of $\angle C$,
$\angle ACY = \angle BCX$ ...(I)
and $AX = AY$

In $\triangle AXY$,
$\angle AXY = \angle AYX$ (Angles opposite to equal sides)...(II)

Now, $\angle XYC = \angle AXB = 180$ (Angles on a straight line)
$\angle AYX + \angle AYC = \angle AXY + \angle BXY$
hence, $\angle AYC = \angle BXY$....(III)

Also, In $\triangle AYC$ and $\triangle BXC$
$\angle AYC + \angle YCA + \angle CAY = \angle BXC + \angle BCX + \angle XBC = 180$ (Angles sum property)
$\angle CAY = \angle XBC$ (From I and III)
or $\angle CAY = \angle ABC$ You're just one step away

TRUE/FALSE Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 87

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