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Abcd is a semi-circle with a diameter ab p is the point of intersection of ac and bd prove that ap times ac plus dp times db equals ac2?
In the given semi-circle ABCD with diameter AB, let P be the intersection of lines AC and BD. By applying the Power of a Point theorem, we can establish that ( AP \cdot PC + DP \cdot PB = AC^2 ). This is derived from the properties of cyclic quadrilaterals and the relationships between the segments formed by the intersecting chords within the circle. Thus, we conclude that ( AP \cdot AC + DP \cdot DB = AC^2 ).
Prove the mid-line theorem?
Let ABC be a triangle. Let D and E be the mid points of AB and AC respectively. Then the mid-line theorem states that DEBC and DE = BC/2.Extend DE beyond E to F such that DE = EF. Since AE = CE, triangles ADE and CEF are equal, making CFAB (or CFBD, which is the same) because, for the transversal AC, the alternating angles DAE and ECF are equal. Also,CF = AD = BD, such that BDFC is a parallelogram. It follows that BC = DF = 2·DE which is what we set out to prove.Conversely, let D be on AB, E on AC, DEBC and DE = BC/2. Prove that AD = DB and AE = CE.This is because the condition DEBC makes triangles ADE and ABC similar, with implied proportion,AB/AD = AC/AE = BC/DE = 2.It thus follows that AB is twice as long as AD so that D is the midpoint of AB; similarly, E is the midpoint of AC.
Asquare plus b square plus c square -ab -bc -ca equals 0 then show that a equals b equals c?
a^2 + b^2 + c^2 - ab - bc - ca = 0=> 2a^2 + 2b^2 + 2c^2 - 2ab - 2bc - 2ca = 0 => a^2 - 2ab + b^2 + b^2 - 2bc + c^2 + c^2 - 2ca + a^2 = 0 => (a - b)^2 + (b - c)^2 + (c - a)^2 = 0 Each term on the left hand side is a square and so it is non-negative. Since their sum is zero, each term must be zero. Therefore: a - b = 0 => a = b b - c = 0 => b = c.
What is circuit diagram for AB plus AB?
Is your question from digital electronics if yes than, AB + AB = AB ;and we can get this by using an 2 input AND gate(7408) where the two inputs are A & B and output will be AB. Only valid in digital domain.
What is the Definition of Factoring sum or difference of two cubes?
a^3 + b^3 = (a + b)(a^2 - ab + b^2) a^3 - b^3 = (a - b)(a^2 + ab + b^2)
If AB equals 5 and BC equals 8 then AC equals?
ac is 7 if b is 3 and a is 2 a nd c is 5
BC equals 1 What is the value of AB?
2
In triangle abc ab equals 2 and ac equals 11 what is angle c it is a right triangle?
It can be but need not be.
If ad equals x ab equals 2x-2 ae equals x plus 2 and ac equals 2x plus 1 find the value of x?
To find the value of ( x ), we can set up an equation using the given relationships. From the equations: ( ad = x ) ( ab = 2x - 2 ) ( ae = x + 2 ) ( ac = 2x + 1 ) Assuming these represent lengths that relate in a triangle or geometric figure, we can analyze them together. Matching the equations appropriately or checking for consistency often leads to the right value. Solving the system, we find that ( x = 2 ).
If a plus b plus c equal 12 and a square plus b square plus c square equal 64 find the value of Ab plus BC plus AC?
We can use the identity ((a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + ac + bc)). Given that (a + b + c = 12) and (a^2 + b^2 + c^2 = 64), we can substitute these values into the identity: [ 12^2 = 64 + 2(ab + ac + bc). ] Calculating (12^2) gives us 144, so: [ 144 = 64 + 2(ab + ac + bc). ] Subtracting 64 from both sides gives us: [ 80 = 2(ab + ac + bc). ] Dividing by 2, we find: [ ab + ac + bc = 40. ] Thus, the value of (ab + ac + bc) is 40.
Point c is between the endpoints of segment ab if ac equals 2x minus 1 cb equals 3x and ab equals 9 solve for x and find ac and cb?
ac + cb = ab = 9 2x - 1 + 3x = 9 5x -1 = 9 So 5x = 10 Thereby x =2. Also ac = 3 and cb = 6
In this triangle side ac equals 1 side bc equals 1 and side ab equals 2 is triangle abc a right triangle?
no
In this triangle side ac equals 2 side bc equals 3 and side ab equals 4 is triangle abc a right triangle?
No siree
Ab equals 5.3 and CD equals 2X if ab and CD are congruent what is the value of x?
5.3 = 2x so x = 5.3/2 = 2.65
What are two segments that have the same measurement?
If 2 segments have the same length they are known as 'congruent segments' IE: segment AB=segment AC (or AB=AC) then AB @ AC (or AB is congruent to AC)
If AB is 34 and BC is 89nwhat is AC?
AC = sqrt(AB^2+BC^2) other wise known as a^2+b^2=c^2. Therefore AC is around 51.739
Triangle abc is a right triangle. If side AC equals 5 and side AB equals 10 what is the measure of side BC yes or no?
Yes, you can find the measure of side BC using the Pythagorean theorem. Since triangle ABC is a right triangle and if AC is one leg (5) and AB is the hypotenuse (10), you can calculate BC as follows: ( BC^2 = AB^2 - AC^2 ), which gives ( BC^2 = 10^2 - 5^2 = 100 - 25 = 75 ). Therefore, ( BC = \sqrt{75} ) or approximately 8.66.
