in triangle ABD angle B is 90° the internal bisector of angle B meets AC at D given that AB= 3cm BC = 4 cm find AD
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Answer:
Let BC=x and AD=y, then as per bisector theorem,
DC
BD
=
AC
AB
=
3
4
Hence,
DC
BD
=
7
4x
,DC=
7
3x
Now in triangle ABD, using cosine rule,
cos30
0
=
2×3y
{4
2
+y
2
−(
49
16x
2
)}
⇒4
3
y={16+y
2
−(
49
16x
2
)} .....(eqn 1)
Similarly in triangle ADC,
cos30
0
=
2×3y
{3
2
+y
2
−(
49
9x
2
)}
⇒3
3
y={9
2
+y
2
−(
49
9x
2
)} .....(eqn 2)
From eqn (1) and (2) we get,
y=
7
12
3
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