I can’t understand why everyone complicates this question. It can be easily solved by similar triangles.
In this png, we have something to make sure.
∠B=∠DAB
∠
B
=
∠
D
A
B
(Yes, dab)
This also means AD=BD
A
D
=
B
D
.
This is our basic construction of D, which is going to help us.
∠ADC=∠DAB+∠B=2∠B=∠CAB
∠
A
D
C
=
∠
D
A
B
+
∠
B
=
2
∠
B
=
∠
C
A
B
∠CAD=∠CAB−∠DAB=∠B
∠
C
A
D
=
∠
C
A
B
−
∠
D
A
B
=
∠
B
These are based on the fact that ∠A=2×∠B
∠
A
=
2
×
∠
B
Actually these conditions suffice. Because I am just proving that △ACD∼△BCA
△
A
C
D
∼
△
B
C
A
Similarity makes us realize the following:
ACBC=ADAB
A
C
B
C
=
A
D
A
B
and
ACBC=CDAC
A
C
B
C
=
C
D
A
C
So
AC×AB=BC×AD
A
C
×
A
B
=
B
C
×
A
D
and
AC2=BC×CD
A
C
2
=
B
C
×
C
D
So
BC2=BC×(BD+CD)=BC×(AD+CD)
B
C
2
=
B
C
×
(
B
D
+
C
D
)
=
B
C
×
(
A
D
+
C
D
)
=AC×AB+AC2
=
A
C
×
A
B
+
A
C
2
Q.E.D.
2.4k Views ·
Answer:
B. ∠1 and ∠8 are parallel
Step-by-step explanation:
identification from the image.
Answer:
Remove backets
Group and Evaluate like terms
Answer: 21600
216 as a percentage of certain number x can be calculated by dividing 216 by x, and multiplying the result by 100. For example, 216 as a percentage of 10 = (216 / 10) x 100% = 2160%.
Step-by-step explanation:
Answer:
a
x
2
+
b
x
+
c
=
0
the formula for the roots is
x
=
−
b
±
√
b
2
−
4
a
c
2
a
(
1
)
Identify the values for
a
,
b
,
&
c
x
2
+
4
x
+
3
=
0
cmp
a
x
2
+
b
x
+
c
=
0
a
=
1
b
=
4
c
=
3
(
2
)
Substitute these numbers into eh formula
x
=
−
4
±
√
4
2
−
(
4
×
1
×
3
)
2
×
1
(
3
)
Carefully proceed and do the calculations
x
=
−
4
±
√
16
−
12
2
x
=
−
4
±
√
4
2
x
=
−
4
±
2
2
now calculate the two separate solutions
x
1
=
−
4
+
2
2
=
−
2
2
=
−
1
x
2
=
−
4
−
2
2
=
−
6
2
=
−
3
Answer link
Step-by-step explanation:
