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Let the base A B of a triangle A B C b...

Let the base `A B` of a triangle `A B C` be fixed and the vertex `C` lies on a fixed circle of radius `rdot` Lines through `Aa n dB` are drawn to intersect `C Ba n dC A ,` respectively, at `Ea n dF` such that `C E: E B=1:2a n dC F : F A=1:2` . If the point of intersection `P` of these lines lies on the median through `A B` for all positions of `A B ,` then the locus of `P` is a circle of radius `r/2` a circle of radius `2r` a parabola of latus rectum `4r` a rectangular hyperbola

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Let the base A B of a triangle A B C be fixed and the vertex C lies on a fixed circle of radius rdot Lines through Aa n dB are drawn to intersect C Ba n dC A , respectively, at Ea n dF such that C E: E B=1:2a n dC F : F A=1:2 . If the point of intersection P of these lines lies on the median through A B for all positions of A B , then the locus of P is (a) a circle of radius r/2 (b) a circle of radius 2r (c) a parabola of latus rectum 4r (d) a rectangular hyperbola

In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley, such that B D=2D Ca n dA E=3E Cdot Let P be the point of intersection of A Da n dB Edot Find B P//P E using the vector method.

In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley, such that B D=2D Ca n dA E=3E Cdot Let P be the point of intersection of A Da n dB Edot Find B P//P E using the vector method.

In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley, such that B D=2D Ca n dA E=3E Cdot Let P be the point of intersection of A Da n dB Edot Find B P//P E using the vector method.

In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley, such that B D=2D Ca n dA E=3E Cdot Let P be the point of intersection of A Da n dB Edot Find B P//P E using the vector method.

Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that A B=B C=r . Find the locus of the point of intersection of tangents at Aa n dCdot

Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that A B=B C=r . Find the locus of the point of intersection of tangents at Aa n dCdot

Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that A B=B C=r . Find the locus of the point of intersection of tangents at Aa n dCdot

Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that A B=B C=r . Find the locus of the point of intersection of tangents at Aa n dCdot

In an isosceles triangle A B C with A B=A C , a circle passing through B\ a n d\ C intersects the sides A B\ a n d\ A C at D\ a n d\ E respectively. Prove that D E || B C .