## In the figure 2.28 seg PS is the median of PQR and PT⊥QR. Prove that,

(1) QS = ½ QR ……(i) [S is the midpoint of QR]SR = ½ QR ……(ii)QS = SR [From (i) and (ii)]PT ⊥QR [Given]PSR is an obtuse angle. [From figure]PR2 = SR2+PS2+2SR×ST …..(iii) [Application of Pythagoras theorem]Substitute SR = ½ QR in (iii)PR2 =[(½)QR]2+PS2+2(1/2)QR×STPR2 =[(½)QR]2+PS2+QR×STPR2 = PS2 + QR×ST +(QR/ 2 )2Hence proved. (ii) PT⊥QS [Given] PSQ is an acute […]

## In ABC, AB = 10, AC = 7, BC = 9 then find the length of the median drawn from point C to side AB

Let CD is the median drawn from C to AB.Given AB = 10AD = (1/2)×AB [D is the midpoint of side AB]AD = 10/2 = 5Since CD is the medianAC2+BC2 = 2CD2+2AD2 [Apollonius theorem]72+92 = 2 CD2+2×522 CD2 = 72+92-2×522 CD2 = 80CD2 = 40Taking square roots on both sidesCD = 2√10Hence the length of median drawn from point C to […]

## In PQR, point S is the midpoint of side QR. If PQ = 11,PR = 17, PS =13, find QR.

Given , S is the midpoint of QR .PS is the median.PQ2+PR2 = 2 PS2+2SR2 [By Apollonius theorem]112+172 = 2×132+2×SR2121+289 = 2×169+2×SR22SR2 = 121+289-3382SR2 = 72SR2 = 72/2 = 36SR = 6Since S is the midpoint of QR , QR = 2SRQR = 2×6 = 12Hence QR = 12 units.