As shown in the figure, given that AB is 2cm longer than AC, the vertical bisector of BC intersects AB at D, crosses BC at e, and the circumference of △ ACD is 14cm, then ab=______ cm，AC=______ cm．

As shown in the figure, given that AB is 2cm longer than AC, the vertical bisector of BC intersects AB at D, crosses BC at e, and the circumference of △ ACD is 14cm, then ab=______ cm，AC=______ cm．

∵ de bisects BC vertically,
∴DB=DC．
∵AC+AD+DC=14cm，
∴AC+AD+BD=14cm，
AC + AB = 14cm
And ∵ AB-AC = 2cm,
Let AB = xcm, AC = YCM
According to the meaning of the title, we get
x+y＝14
x−y＝2 ，
The solution
x＝8
y＝6
The length of AB is 8cm and that of AC is 6cm

As shown in the figure, ∠ C = 90 ° in △ ABC, the vertical line De of AB intersects AB at e and BC at D. if AB = 10 and AC = 6, then the circumference of △ ACD is () A. 16 B. 14 C. 20 D. 18

In ∵ ABC, ∵ C = 90 °, ab = 10, AC = 6,
∴BC=
AB2−AC2=
102−62=8，
∵ De is the vertical bisector of line ab,
∴AD=BD，
/ / AD + CD = BD + CD, that is, AD + CD = BC,
The circumference of △ ACD = AC + CD + ad = AC + BC = 6 + 8 = 14
Therefore, B

As shown in the figure, given that AB is 2cm longer than AC, the vertical bisector of BC intersects AB at D, crosses BC at e, and the circumference of △ ACD is 14cm, then ab=______ cm，AC=______ cm．

∵ de bisects BC vertically,
∴DB=DC．
∵AC+AD+DC=14cm，
∴AC+AD+BD=14cm，
AC + AB = 14cm
And ∵ AB-AC = 2cm,
Let AB = xcm, AC = YCM
According to the meaning of the title, we get
x+y＝14
x−y＝2 ，
The solution
x＝8
y＝6
The length of AB is 8cm and that of AC is 6cm

As shown in the figure, in △ ABC, ab = AC, De is the vertical bisector of AB, the perimeter of △ BCE is 24cm, and BC = 10cm. Calculate the length of ab

It is known that BC + be + CE = 24,
∵BC=10，
∴BE+CE=14，
∵ de bisects AB vertically,
∴AE=BE，
∴AE+CE=14，
AC = 14,
∵AB=AC，
∴AB=14．

As shown in the figure, in the triangle ABC, ab = AC, and the vertical bisector of AB intersects AC at point E. given that the circumference of triangle BCE is 8, ac-bc = 2, calculate the lengths of AB and BC 01

The solution ∵ De is the vertical bisector of ab
ν be = AE (the distance from the point on the vertical bisector to the two ends of the line segment is equal)
∵ the circumference of the triangle BCE is 8
Namely: △ BCE perimeter
=BC+CE+BE
=BC+CE+AE
=BC+AC
=8
And ∵ ac-bc = 2
∴AC=AB=5 BC=3
If there is anything you don't understand, you can ask,

In the triangle ABC, ab = AC, De is the vertical bisector of AB, and the circumference of triangle BCE is 14, BC = 6. Find the length of ab

First draw a picture,
Because De is the vertical bisector of ab,
Therefore, be = AE (the distance from the point on the vertical bisector to both ends of the line segment is equal)
S=BC+CE+EA=BC+AC=14
And BC = 10
So, AC = 14-10 = 14
AB=AC=4

As shown in the figure, in △ ABC, AC = 8cm, ed bisects AB vertically. If the circumference of △ EBC is 14cm, then the length of BC is______ cm．

Because ed bisects AB vertically,
So AE = be
Then the circumference of △ EBC is BC + CE + EB = BC + CE + EA = BC + (CE + EA) = BC + AC
Because the circumference of △ EBC is 14 cm,
So BC + AC = 14,
BC + 8 = 14
So BC = 6cm, BC = 6cm

In △ ABC, the vertical bisector of edge BC intersects AB and BC at points E and D respectively, and the circumference of △ AEC is 13, and AB-AC = 3 As soon as possible,

The circumference of △ AEC is 13
Namely
∵ e is the point on the vertical bisector of BC
/ / CE = be (the distance from the point on the vertical bisector to the two ends of the line segment is equal)
∴AC+AE+BE=AC+AB=13
And ∵ AB-AC = 3
∴AB=8 AC=5

As shown in the figure, in △ ABC, if AB = a, AC = B, the vertical bisector de on the edge of BC intersects BC and BA at points D and e respectively, then the perimeter of △ AEC is equal to () A. a+b B. a-b C. 2a+b D. a+2b

∵ ed vertical and bisecting BC,
∴BE=CE．
AB=a，AC=b．
∴AB=AE+BE=AE+CE=a
The circumference of △ AEC is AE + EC + AC = a + B
Therefore, a

As shown in the figure: the circumference of △ ABC is 24cm, ab = 10cm, the vertical bisector De of edge AB intersects BC, the edge is at point E, and the perpendicular foot is D, calculate the circumference of △ AEC

The vertical bisection is ab
 be = AE (2 points)
The circumference of △ ace = AE + EC + AC = be + CE + AC = BC + AC
The circumference of ABC is 24cm, ab = 10cm
∴BC+AC=24-10=14cm
The circumference of ACE is 14 cm