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

#### Realted Questions

Q1 Subjective Medium
$\overleftrightarrow{AB}$ || $\overleftrightarrow{CD}$ in the following figure. $\overleftrightarrow{XY}$ is the transversal. If $m \angle PQA = 140^o$, find the measure of remaining angles:

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Single Correct Medium
In the given figure, AB$||$CD and BC$||$DE, then the value of x is _____________.
• A. $90^o$
• B. $85^o$
• C. $80^o$
• D. $95^o$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Subjective Medium
Write the complement of:

$21^o \quad 17'$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Single Correct Medium
Straight angle is-
• A. $\displaystyle 30^{0}$
• B. $\displaystyle 45^{0}$
• C. $\displaystyle 120^{0}$
• D. $\displaystyle 180^{0}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Single Correct Medium
In the given figure, magnitude of angles shown are:
• A. $\displaystyle 40^{\circ},135^{\circ}$
• B. $\displaystyle 45^{\circ},130^{\circ}$
• C. $\displaystyle 180^{\circ}$
• D. $\displaystyle 45^{\circ},135^{\circ}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020