[" point on hypotenuse such th"],[" C.If "DP perp AB" and "DQ perp BC" the "],[" tat "]

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 .

Let A B C be a triangle and D and E be two points on side A B such that A D=B E . If DP || BC and EQ || AC , Then prove that PQ || AB .

In Figure,AB and AC are two equal chords of a circle whose centre is O .If OD perp AB and OE perp AC, prove that ADE is an isosceles triangle.

Fig.4.134,ABC is a right triangle right angled at B and D is the foot of the wedicular dnem from Ben AC. If DM perp BC and DN perp AB, prove that ( i )DM^(2)=DN xx MC( ii) DN^(2)=DM xx AN

In Delta ABC and D is the mid point of BC If DL perp AB and DM perp AC such that DL=DM prove that AB=AC

O is a point in the interior of /_PQR such that OM perp QR and ON perp QP ,if /_PQR=60^(@), then find the value of /_NOM

ABCD is a rectangle.Points M and N are on BD such that AM perp BD and CN perp BD Prove that BM^(2)+BN^(2)=DM^(2)+DN^(2)

In Fig.4.98, if AB perp BC and DE perp AC Prove that ABC-AED.( FIGURE )

In ABC, if BD perp AC and BC^(2)=2ACCD, then prove that AB=AC .

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