Circle O has diameters AB and CD perpendicular to each other. AM is any chord intersecting CB at N.I is the center of the circle inscribed in triangle AMB. Prove that M, I, D are collinear points
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Given acute triangle ABC(AB<AC). O is the midpoint of BC, BM and CN are the altitudes of triangle ABC. The bisectors of angle \(\widehat{BAC}\)and \(\widehat{MON}\)meet each other at D. AD intesects BC at E. Prove that quadrilateral BNDE is inscribed in a circle.s
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EXERCISE 2: Let ABC be a triangle with p/g of angles B and C intersecting at I. The exterior bisector of two angles B and C intersect at prove that the three points A,I,H are collinear
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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 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 \(BD⊥BC\)
Given a triangle ABC having BAC = 1200, and AC= 2AB. The line passing through A perpendicular to AC intersects the perpendicular bisector of BC at O. Prove that the triangle OBC is an equilateral triangle
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12 tháng 1 2022 lúc 19:26
Given a circle (O) and its diameter AB. C is a point on the circle which is different from A and B. H is the projection of C on AB. I is the midpoint of CH. The line passes through I and perpendiculars with OC cut (O) at 2 points D and E. Prove that \(\Delta CDH\)is an isosceles triangle.
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Nose this my is các anh chị giải dùm em với
too easy for me, teacher :)))
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Give the quadrilateral ABCD. \(A_1,B_1,C_1,D_1\) is the center of the circle circumscribed to the triangle BCD, CDA, DAB, ABC. \(A_2,B_2,C_2,D_2\) is the center of the circle circumscribed to the triangle \(B_1C_1D_1,C_1D_1A_1,D_1A_1B_1,A_1B_1C_1\). Prove that : \(\frac{S_{A_2B_2C_2D_2}}{S_{ABCD}}=\frac{\left(cotA+cotC\right)^2\left(cotB+cotD\right)^2}{16}\)
Given the Triangle ABC and the point M inside the triangle (M don't belong on any sides of triangle).let I be the intersection point of the line BM and the side AC
a, compare MA to MI+MB,then prove that MA +MB<IB+IA
b, compare IB to IC+CB, then prove that IB+IA<CA+CB
c, Demonstrate the inequality MA+MB<CA+CB
Given the Triangle ABC and the point M inside the triangle (M don't belong on any sides of triangle).let I be the intersection point of the line BM and the side AC
a, compare MA to MI+MB,then prove that MA +MB<IB+IA
b, compare IB to IC+CB, then prove that IB+IA<CA+CB
c, Demonstrate the inequality MA+MB<CA+CB
Môn j mà hay zâỵ sao dịch dc lên gogle dịch à
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8 tháng 1 2022 lúc 21:07
Let I be the incentre of acute triangle ABC with ABne AC. The incircle omegaof ABC is tangent to sides BC, CA and AB at D, E, F respectively. The line through D pependicular to EF meets omegaagain at R. Line AR meets omegaagain at P. The circumcircles of triangles PCE and PBF meet again at Q. Prove that lines DI and PQ meet on the line through A perpendicular to AI.
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Let I be the incentre of acute triangle ABC with \(AB\ne AC\). The incircle \(\omega\)of ABC is tangent to sides BC, CA and AB at D, E, F respectively. The line through D pependicular to EF meets \(\omega\)again at R. Line AR meets \(\omega\)again at P. The circumcircles of triangles PCE and PBF meet again at Q. Prove that lines DI and PQ meet on the line through A perpendicular to AI.