Answer:
In △ABD,
AB
2
=BD
+AD
(Pythagoras theorem)
In △ACD,
AC
=CD
Add both the equations,
+AC
+CD
BC
+2BD×CD−2BD×CD+2AD
(Apply pythagoras theorem to triangle ABC)
=(BD+DC)
−2BD×CD+2AD
=BC
AD
=BD×CD
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Answers & Comments
Answer:
In △ABD,
AB
2
=BD
2
+AD
2
(Pythagoras theorem)
In △ACD,
AC
2
=CD
2
+AD
2
(Pythagoras theorem)
Add both the equations,
AB
2
+AC
2
=BD
2
+AD
2
+CD
2
+AD
2
BC
2
=BD
2
+AD
2
+2BD×CD−2BD×CD+2AD
2
(Apply pythagoras theorem to triangle ABC)
BC
2
=(BD+DC)
2
−2BD×CD+2AD
2
BC
2
=BC
2
−2BD×CD+2AD
2
AD
2
=BD×CD