In Fig. 4.121, `A B C` is a right triangle right angled at `B` and `D` is the foot of the the perpendicular drawn from `B` on `A C` . If `D M_|_B C` and `D N_|_A B` , prove that: (FIGURE) `D M^2=D NxxM C` (ii) `D N^2=D MxxA N`

In fig., D is a point on hypotenuse AC of DeltaA B C ,D M_|_B C and D N_|_A B . Prove that (i) D M^2=D N*M C (ii) D N^2=D M*A N

In fig.41, A B C is a right triangle right angled at Adot D lies on B A produced and D E_|_B C , intersecting A C at F . if /_A F E=130^0, find /_B D E (ii) /_B C A /_A B C

In Figure, ABD is a triangle right-angled at A and A C_|_B D . Show that (i) A B^2=B C.B D (ii) A C^2=B C.D C (iii) A D^2=B D.C D

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ A M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: \ F C B~=\ A C E

In Figure, B M a n d D N are both perpendiculars to the segments A C a n d B M=D N . Prove that A C bisects B D

A B D is a right triangle right-angled at A and A C_|_B D . Show that A B^2=B CdotB D (ii) A C^2=B CdotD C (iii) A D^2=B DdotC D (iv) (A B^2)/(A C^2)=(B D)/(D C)

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ A M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: a r(C Y X E)=a r\ (A C F G)

In Fig. 5.10, if A C=B D , then prove that A B=C D .

In right triangle A B C , right angle at C , M is the mid-point of the hypotenuse A Bdot C is jointed to M and produced to a point D such that D M=C Ddot Point D is joined to point Bdot Show that A M C~= B M D (ii) /_D B C=/_A C B D B C~= A C B (iii) C M=1/2A B

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ A M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: a r\ (B Y X D)=2\ a r\ (\ M B C)