The Total solution for NCERT class 6-12
In Figure, PS is thebisector of ∠ QPR of ∆ PQR. Provethat QS/PQ = SR/PR
Answer - 1 : -
Answer - 2 : -
In Figure, ABC is atriangle in which ∠ABC > 90° and AD ⊥ CB produced. Prove that
AC2= AB2+BC2+ 2 BC.BD.
Answer - 3 : -
In Figure, ABC is atriangle in which ∠ ABC < 90° and AD ⊥ BC.
Answer - 4 : -
Prove that
AC_2= AB_2+ BC_2 – 2 BC.BD.
In Figure, AD is amedian of a triangle ABC and AM ⊥ BC.
Answer - 5 : -
Prove that :
(i) AC_2 = AD_2 + BC.DM + 2 (BC/2)_ 2
(ii) AB_2 = AD_2 – BC.DM + 2 (BC/2)_ 2
(iii) AC_2 + AB_2 = 2 AD_2 + ½ BC_2
Solution
Prove that the sumof the squares of the diagonals of parallelogram is equal to the sum of thesquares of its sides.
Answer - 6 : -
In Figure, twochords AB and CD intersect each other at the point P. Prove that :
Answer - 7 : -
(i) ∆APC ~ ∆ DPB
(ii) AP . PB = CP . DP
In Fig. 6.62, twochords AB and CD of a circle intersect each other at the point P (whenproduced) outside the circle.
Answer - 8 : -
Prove that:
(i) ∆ PAC ~ ∆ PDB
(ii) PA . PB = PC . PD.
In Figure, D is apoint on side BC of ∆ ABC such that BD/CD = AB/AC. Prove that AD is thebisector of ∠ BAC.
Answer - 9 : -
Nazima is flyfishing in a stream. The tip of her fishing rod is 1.8 m above the surface ofthe water
Answer - 10 : - and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, how much string does she have out (see Figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?