ABC is a triangle in which AB = AC and D is a point on AC such that = AC x CD. Prove that BD = BC.
Answers
Answered by
1
Answer:
Given△ABC in which AB=AC and D is a point on the side AC such that
BC
2
=AC×CD
To prove: BD=BC
construction: join BD
we have,
BC
2
=AC×CD
⇒
CD
BC
=
BC
AC
............(i)
Thus, in △ABC and △BDC, we have
BC
AC
=
CD
BC
[From (i)] and,
∠C=∠C [Common]
∴ △ABC∼△BDC [By SAS criterion of similarity]
⇒
BD
AB
=
DC
BC
⇒
BD
AC
=
CD
BC
[∵ AB=AC]
⇒
BC
AC
=
CD
BD
.............(ii)
From (i) and (ii), we get
CD
BC
=
CD
BD
⇒BD=BC
Similar questions