If `A(x_1,y_1),B(x_2,y_2) and C(x_3,y_3)` are the vertices of traingle ABC and `x_(1)^(2)+y_(1)^(2)=x_(2)^(2)+y_(2)^(2)=x_3^(2)+y_(3)^(2)`, then show

Question

If `A(x_1,y_1),B(x_2,y_2) and C(x_3,y_3)` are the vertices of traingle ABC and `x_(1)^(2)+y_(1)^(2)=x_(2)^(2)+y_(2)^(2)=x_3^(2)+y_(3)^(2)`, then show

If `A(x_1,y_1),B(x_2,y_2) and C(x_3,y_3)` are the vertices of traingle ABC and `x_(1)^(2)+y_(1)^(2)=x_(2)^(2)+y_(2)^(2)=x_3^(2)+y_(3)^(2)`, then show that `x_1 sin2A+x_2sin2B+x_3sin2C=y_1sin2A+y_2sin2B+y_3sin 2C=0`.

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Related Questions

If `x_1a n dx_2` are the roots of the equation `e^2 x^(lnx)=x^3` with `x_1> x_2,` then `x_1=2x_2` (b) `x_1=x2 2` `2x_1=x2 2` (d) `x1 2=x2 3`

2 Answers 4 Views

If `P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4)` are four concyclic points on the rectangular hyperbola ) and `xy = c^2` , then coordinates of the

2 Answers 4 Views

If `sin^(-1)x_i in [0,1]AAi=1,2,3, .28` then find the maximum value of `sqrt(sin^(-1)x_1)sqrt(cos^(-1)x_2)+sqrt(sin^(-1)x_2)sqrt(cos^(-1)x_3)+` `sqrt(

2 Answers 5 Views

Let `A_1,A_2,A_3,...,A_n` are n Points in a plane whose coordinates are `(x_1,y_1),(x_2,y_2),....,(x_n,y_n)` respectively. `A_1A_2` is bisected at the

2 Answers 5 Views

The vertices of a triangle are `A(x_1,x_1tantheta_1),B(x_2, x_2tantheta_2),` and `C(x_3, x_3tantheta_3)dot` If the circumcenter of ` A B C` coincides

2 Answers 5 Views

If `(x_i,y_i),i=1,2,3` are the vertices of an equilateral triangle such that `(x_1+2)^2+(y_1-3)^2=(x_2+2)^2+(y_2-3)^2=(x_3+2)^2+(y_3-3)^2`, then find

2 Answers 4 Views

If `|x_1y_1 1x_2y_2 1x_3y_3 1|=|a_1b_1 1a_2b_2 1a_3b_3 1|` then the two triangles with vertices `(x_1, y_1),(x_2,y_2),(x_3,y_3)` and `(a_1,b_1),(a_2,b

2 Answers 5 Views

If the point `x_1+t(x_2-x_1),y_1+t(y_2-y_1)` divides the join of `(x_1,y_1)` and `(x_2,y_2)` internally then

2 Answers 5 Views

Normals at two points `(x_1y_1)a n d(x_2, y_2)` of the parabola `y^2=4x` meet again on the parabola, where `x_1+x_2=4.` Then `|y_1+y_2|` is equal to `

2 Answers 4 Views

In `DeltaABC,BC=1,sin.(A)/2=x_1,sin.(B)/2=x_2,cos.(A)/2=x_3andcos.(B)/2=x_4" with "(x_1/x_2)^2007-(x_3/x_4)^2006=0` If `angleA=90^@`, then area of `De

2 Answers 5 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Since `x_(1)^(2)+y_(1)^2=x_(2_^2=x_(3)^2`, circumcentre of `DeltaABC` is `(0,0)`.
Now, coordinates of circumcentre are
`((x_1sin2A+x_2sin2B+x_3sin2C)/(sin2A+sin2B+sin2C),(y_1sin2A+y_2sin2b+y_3sin2C)/(sin2A+sin2B+sin2C))=(0,0)`
Therefore,`x_1sin2A+x-2sin2B+x_3sin2C=y_1sin2A+y_2sin2B+y_3sin2C=0`

4 views Answered 2023-02-05 15:29