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 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.
Said quadrangle ABCD for the measurement of the angle A; B; C; D proportional voi5; 8; 13va 10.A / Count measure the angles of a quadrilateral ABCDb / Extend sides AB and DC intersect at E, which lasted two sides AD and BC in F. Two-rays catnhau sense of angles AED and corner cutting AFB O. Separate each corner giaccua AFB cutting edge CD and AB at M and N. Prove cuadoan MN O is the midpoint.
Said quadrangle ABCD for the measurement of the angle A; B; C; D proportional voi5; 8; 13va 10.A / Count measure the angles of a quadrilateral ABCDb / Extend sides AB and DC intersect at E, which lasted two sides AD and BC in F. Two-rays catnhau sense of angles AED and corner cutting AFB O. Separate each corner giaccua AFB cutting edge CD and AB at M and N. Prove cuadoan MN O is the midpoint.
Said quadrangle ABCD for the measurement of the angle A; B; C; D proportional voi5; 8; 13va 10.A / Count measure the angles of a quadrilateral ABCDb / Extend sides AB and DC intersect at E, which lasted two sides AD and BC in F. Two-rays catnhau sense of angles AED and corner cutting AFB O. Separate each corner giaccua AFB cutting edge CD and AB at M and N. Prove cuadoan MN O is the midpoint.
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?
with triangle ABC, d is the line passing through B, E of AC. Via E draw straight lines parallel to AB and BC cut d at M, N. D is the intersection of ME and BC. NE lines cut AB and MC at F and K. CMR AFN triangles are in the same form as the MDC triangle