In △ ABC, ab = AC, ∠ BAC = 120 °, the vertical bisector of AB intersects BC at D, and BD = 10cm, then DC=_________ .

In △ ABC, ab = AC, ∠ BAC = 120 °, the vertical bisector of AB intersects BC at D, and BD = 10cm, then DC=_________ .

The vertical bisector of AB intersects AB with E
Let AB = AC, ∠ BAC = 120 degree
And △ BDE ≌ ade
Therefore, ACB = ABC = bad = 30 degree
So, DAC = 90 degree
Because BD = 10
So ad = 10
Because ∠ ACB = 30 degree
So CD = 20

In △ ABC, ab = AC, ∠ BAC = 120 °, the vertical bisector of AB intersects at point D, the perpendicular foot is point E, and de = quarter DC is proved

Connect ad because ∠ BAC = 120 ° and ab = AC, so ∠ ABC = ∠ ACB = 30 ° and ED is the middle vertical line, then ad = BD, so ∠ bad = ∠ abd = 30 ° and ∠ DAC = 90 ° in △ AED, ed = 1 / 2ad, ad = 1 / 2dc and ED = 1 / 2ad, because ∠ AED is right angle tangent, ead = 30 ° and ED = 1 / 2ad

As shown in the figure, in △ ABC, the vertical bisector of BC intersects AB at point E. if the perimeter of △ ABC is 10 and BC = 4, then the perimeter of △ ace is______ ．

The vertical bisector of ∵ BC intersects AB at point E, ∵ be = CE, ∵ ABC has perimeter of 10, BC = 4, ∵ ace has perimeter of AE + CE + AC = AE + be + AC = AB + AC = AB + AC + bc-bc = 10-4 = 6