Question

In the triangle OAB, OA=a and OB=b. M is the midpoint of AB and N is the point on OB such that ON:NB = 1:4. OM meets AN at P.

(a) Find and expression for OP in terms of a and b

(b) Deduce that AP:PN = 5:1.

Answer #1

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In an isosceles triangle ABC ,AB=BC,angle B=20 . M and N are on
AB and BC respectively such that angle MCA =60, angle NAC =50.find
angle MNC

ABC is a right-angled triangle with right angle at A, and AB
> AC. Let D be the midpoint of the side BC, and let L be the
bisector of the right angle at A. Draw a perpendicular line to BC
at D, which meets the line L at point E. Prove that
(a) AD=DE; and
(b) ∠DAE=1/2(∠C−∠B)
Hint: Draw a line from A perpendicular to BC, which meets BC in
the point F

Triangle ABC is a right angle triangle in which
∠B = 90 degree, AB = 5 units , BC = 12 units. CD
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respectively which intersects each other at point I. Find the area
of the triangle DIE.

Let 4ABC be an isosceles triangle, where the congruent
sides are
AB and AC. Let M and N denote points on AB and AC
respectively
such that AM ∼= AN. Let H denote the intersection point of MC
with
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If ?ABC is an isosceles triangle where AB¯?AC¯, m?A=(2x?20)°,
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from B onto CM.
a) Find the lengths of P B and PM.
b) Find the area of ABPM.
c) Consider now ABCD being a parallelogram. Denote by M the
midpoint of side AD and by P the leg of the perpendicular from B
onto CM. Prove that AP =...

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(§2.1) Let a,b,p,n ∈Z with n > 1.
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by columns of the two matrix. For instance, if A is 3 × 4 and B is...

Linear Algebra question:Suppose A and B are invertible
matrices,with A being m*m and B n*n.For any m*n matrix C and any
n*m matrix D,show that:
a)(A+CBD)-1-A-1C(B-1+
DA-1C)-1DA-1
b) If A,B and A+B are all m*m invertible matrices,then deduce
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(A+B)-1=A-1-A-1(B-1+A-1)-1A-1

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