In the figure given below D is a point on hypotenuse AC of `DeltaABC ` such that BD `bot ` AC DM `bot ` BC and DN `bot ` AB .Prove that :

(i) `DM^(2)= DNxx MC ` (ii) `DN^(2) = DM xx AN`

In a right tringle ABC, right-angled at B, D is a point on hypotenuse such that BD bot AC . If DP bot AB and DQ bot BC then prove that (a) DQ^(2)=DP*QC" " DP^(2)=DQ*AP .

In the figure given below O is a point in the interior of a triangle ABC , OD bot BC ,OE bot AC and OF bot AB . Show that AF^(2) +BD^(2)+CE^(2)=AE^(2)+CD^(2)+BF^(2)

In the figure given below ABC is a triangle right angled at A and AC bot BD . Show that AB^(2) = BC xx BD

AB botBC and DE bot AC . Prove that DeltaABC ~ DeltaAED .

In the figure given below ABC is a triangle right angled at A and AC bot BD . Show that AD^(2) = BD xx DC

In the figure given below ABC is a triangle right angled at A and AC bot CD . Show that AC^(2) = BC xx DC

In Fig.4.121,ABC is a right triangle right angled at B and D is the foot ot the the perpendicular drawn from B on AC .If DM perp BC and DN perp AB ,prove that: (FIGURE) DM ^(2)=DN xx MC( ii) DN^(2)=DM xx AN

In the given figure, E is a point on side CB produced of an isosceles Delta ABC with AB=AC. . If AD bot BC and EF bot AC , prove tha Delta ABD~ Delta ECF

In the given figure, DB bot BC, DE bot AB and AC bot BC . Prove that (BE)/(DE)=(AC)/(BC)

In triangle ABC , angle ACB = 90^(@) , CD bot AB and DE bot CB Prove that CD^(2) xxAC = AD xx AB xxDE .