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triangle ABC is a right angled triangle at C. If D is mid point of bc then prove that ; AB 2 =4AD 2 -3AC 2

triangle ABC is a right angled triangle at C. If D is mid point of bc then prove that ; AB2 =4AD2-3AC2

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2 Answers

kaushik kashyap
20 Points
9 years ago
      look sakshi, please solve this problem by drawing a neat diagram.                        it is given that triangle ABC is a right angled triangle right angled at C and D is the mid point of bc .                                                                                                  by applying pythagoras theorem in triangle ABC , we get                                      AB2=AC2+BC2                                                                                                                =AC2+(2CD)2   (SINCE D IS THE MID POINT OF BC)                                         =AC2+4CD2                                                                                                            =AC2+4(AD2_AC2) ( SINCE IN TRIANGLE ACD WE GET      AD2=AC2+CD2)                                                                                                                            =AC2+4AD2_4AC2                                                                                                 =4AD2_3AC2                                                                                                        THEREFORE , AB2=4AD2_3AC2.                                                            THANK YOU .                                                                                                           KAUSHIK.
Yash Chourasiya
askIITians Faculty 256 Points
3 years ago
Dear Student

643-523_Untitled.png
From right triangle ACB,
By Pythagoras Theoremwe have,
AB2= AC2+ BC2
AB2= AC2+ (2CD)2[since BC = 2CD]
AB2= AC2+ 4CD2
AB2= AC2+ 4(AD2- AC2) [From right △ACD]
AB2= 4AD2- 3AC2.
Hence Proved

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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