Given the isosceles triangle ABC (AB=AC) with . Draw the bisector AD and BE of angles A and B respectively. Given BE = 10cm. Evaluate AD.

Câu 10:
Given the isosceles triangle ABC (AB=AC) with . Draw the bisector AD and BE of angles A and B respectively. Given BE = 10cm. Evaluate AD.
Answer: AD =  cm.

1.  Two bisector BD and CE of the triangle ABC intersect at O. Suppose that BD.CE = 2BO.OC . Denote by H the point in BC such that .\(OH⊥BC\) . Prove that AB.AC = 2HB.HC

2. Given a trapezoid ABCD with the based edges BC=3cm , DA=6cm ( AD//BC ). Then the length of the line EF ( \(E\in AB,F\in CD\) and EF // AD ) through the intersection point M of AC and BD is ............... ?

3. Let ABC be an equilateral triangle and a point M inside the triangle such that \(MA^2=MB^2+MC^2\) . Draw an equilateral triangle ACD where \(D\ne B\) . Let the point N inside \(\Delta ACD\) such that AMN is an equilateral triangle. Determine \(\widehat{BMC}\) ?

4. Given an isosceles triangle ABC at A. Draw ray Cx being perpendicular to CA, BE perpendicular to Cx \(\left(E\in Cx\right)\) . Let M be the midpoint of BE, and D be the intersection point of AM and Cx. Prove that \(BD⊥BC\)

Given a trapezoid ABCD with base , and . Let M, N be respectively the midpoints of the segments . Evaluate MN.
Answer: cm