[" 24.In Fig."7.220,D" is the mid-point of side "BC" and "AE perp BC" .If "BC=aAC=b" ,"],[AD=p" and "AE=h" ,prove that: "],[" (i) "b^(2)=p^(2)+ax+(a^(2))/(4)quad " (ii) "c^(2)=p^(2)-ax+(a^(2))/(4)]

In the given figure, D is the midpoint of side BC and AE bot BC . If BC=a, AC =b, AB= c, ED =x AD=p and AE =h prove that (i) b^(2)=p^(2)+ax +(a^(2))/(4) (ii) c^(2)=p^(2)-ax+(a^(2))/(4) (iii) (b^(2)+c^(2))=2p^(2)+(1)/(2)a^(2) (iv) (b^(2)-c^(2))=2ax .

D is the mid point of side BC and AE bot BC . If BC=a, AC= b, AB=c, ED=x, AD=p and AE=h, prove that (i) b^(2)=p^(2)+ax+(a^(2))/(4) (ii) c^(2)=p^(2)-ax+(a^(2))/(4) (iii) b^(2)+c^(2)=2p^(2)+(a^(2))/(2)

In Fig. 4.220, D is the mid-point of side B C and A E_|_B C . If B C=a , A C=b , A B=c , E D=x , A D=p and A E=p and A E=h , prove that: (FIGURE) b^2=p^2+a x+(a^2)/4 (ii) c^2=p^2-a x+(a^2)/4 (iii) b^2+c^2=2 p^2+(a^2)/2

In Fig. 4.220, D is the mid-point of side B C and A E_|_B C . If B C=a ,\ \ A C=b ,\ \ A B=c ,\ \ E D=x ,\ \ A D=p and A E=p and A E=h , prove that: (FIGURE) b^2=p^2+a x+(a^2)/4 (ii) c^2=p^2-a x+(a^2)/4 (iii) b^2+c^2=2\ p^2+(a^2)/2

P and Q are the mid-points of the sides CA and CB respectively of a triangleABC , right angled at C, prove that. (i) 4AQ^(2)=4AC^(2)+BC^(2) (ii) 4BP^(2)=4BC^(2)+AC^(2)

In figure, P is the mid-point of side BC of a parallelogram ABCD such that angleBAP=angleDAP . Prove that AD = 2CD.

In fig. P is the mid point of side BC of a parallelogram ABCD such that angleBAP=angleDAP prove that AD=2CD

In a triangle ABC,AC>AB,D is the mid- point of BC and AE perp BC .Prove that: (i) AB^(2)=AD^(2)-BCDE+(1)/(4)BC^(2)( (ii) AB^(2)+AC^(2)=2AD^(2)+(1)/(2)BC^(2)

If a, b, c are in A.P., then prove that : (i) ab+bc=2b^(2) (ii) (a-c)^(2)=4(b^(2)-ac) (iii) a^(2)+c^(2)+4ca=2(ab+bc+ca).

If a, b, c are in A.P., then prove that : (i) ab+bc=2b^(2) (ii) (a-c)^(2)=4(b^(2)-ac) (iii) a^(2)+c^(2)+4ca=2(ab+bc+ca).