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Let ABCD be a trapezoid with bases AB, CD and O be the intersection of AC and BD. If the areas of triangle OAB, triangle OCD are 16cm2, 40cm2respectively and M is the midpoint of BD, then the area of the triangle AMD is .........cm2.
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 BC3cm , DA6cm ( AD//BC ). Then the length of the line EF ( Ein AB,Fin 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^2MB^2+MC^2 . Draw an equilateral triangle ACD whe...
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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 \(BD⊥BC\)
A trapezuim ABCD has two parallel sides AB and CD. The diagonals AC and BD intersect at E. If the areas of triangle CDE and CDB are 1 and 4 respectively, what is the area of the trapezuim ABCD
Given the right triangle ABC (A^ = 90o), BD is the bisector of the angle at B ( D of AC ). If AD = 6cm and AB = 12cm then the area of the right triangle ABC is ...... cm2.
Given the right triangle ABC (A^ = 90o), BD is the bisector of the angle at B ( D of AC ). If AD = 6cm and AB = 12cm then the area of the right triangle ABC is ...... cm2.
Given the right triangle ABC (A^ = 90o), BD is the bisector of the angle at B ( D of AC ). If AD = 6cm and AB = 12cm then the area of the right triangle ABC is ...... cm2.
Given that ABCD is a rectangle with AB = 12 cm, AD = 6 cm. M and N are respectively midpoint of segments BC and CD. Find the area of triangle AMN in square centimeters.
In triangle ABC, BC=AC and BCA=900. D and E are points on AC and AB respectively such that AD=AE and 2CD =BE.Let P be the point of intersection of BD with the bisector of angle CAB. What is the angle PCB in degrees?
Let ABC be an isoceles triangle (AB = AC) and its area is 501cm2. BD is the internal bisector of the angle ABC (D ∈ AC), E is a point on the opposite ray of CA such that CE = CB. I is a point on BC such that CI = 1/2 BI. The line EI meets AB at K, BD meets KC at H. Find the area of the triangle AHC.
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