In the triangle ABC, the bisector of `/_A` intersects BC at X. XL and XM are perpendiculars from X on AB and AC respectively. Prove that `AL= AM`.

O is a point in the interior of ∆ABC . OD,OE and OF are the perpendicular drawn to the sides BC, CA and AB respectively. Prove that AF^2+BD^2+CE^2=AE^2+BF^2+CD^2 .

A line segment drawn parallel to the base BC of ∆ABC intersects AB and AC at X and Y respectively. If X divides AB in 8:3 and AC = 8.8 then prove that AY = 6.4 and YC = 2.4 .

A line segment drawn parallel to the base BC of ∆ABC intersects AB and AC at X and Y respectively. If AB = 4 , AC = 3 and AY = 1.8 then prove that BX= 1.6 .

Line segment drawn parallel to the base BC of ∆ABC cuts AB and AC at D and E respectively. DP , AL and EQ are perpendicular on BC. Prove that LP : PB = LQ : QC .

A line segment drawn parallel to the base BC of ∆ABC intersects AB and AC at X and Y respectively. If AB = 7.2 , AC = 4.8 and AX = 4.2 then show that AY = 2.8 .

A line drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. If AQ : QC = 7: 4 and AB = 8.8 then determine AP and PB.

If Fig. 6.3 ,ABC and AMP are two right triangles right angled at B and M respectively.Prove that : (ii) (CA)/(PA)=(BC)/(MP)

A line drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. If AB = 20 , AC = 15 and AQ = 9 then determine BP.

A line drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. If AB = 12 , AP = 4 , QC = 5 then determine AQ.

A circle is touching the side BC of /_\ABC at P and touching AB and AC produced at Q and R are respectively. Prove that AQ=1/2(AB+BC+CA)=1/2(Perimeter of /_\ABC) .