a circle touches the sides BC CA AB of triangle abc at the point D E F respectively the radius of circle is 4 BD = 8 CD = 6 find AB and AC
Answers
In isosceles triangle ABC, AB=AC; a circle drawn taking AB as diameter meets the side BC at the point D. IF BD=4cm,let us find the value of CD?
Answer
B
D
=
C
D
=
4
c
m
Given AB = AC, BD = 4 cm. Also AB is the diameter of the circle with D on the circumference.
Construction : Join AD
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In triangle ABD,
A
ˆ
D
B
=
90
0
as angle in a semicircle is a right angle.
A
B
2
=
A
D
2
+
B
D
2
Eqn (1)
Now let us consider triangle ACD.
A
ˆ
D
C
=
90
0
as
A
ˆ
D
B
=
90
0
Therefore,
A
C
2
=
A
D
2
+
C
D
2
Eqn (2)
Compare equations (1) & (2),
Given : AB = AC
∴
A
D
2
+
B
D
2
=
A
D
2
+
C
D
2
B
D
2
=
C
D
2
or
B
D
=
C
D
=
4
cm
Answer:
yo yo honey singer
A circle touches the sides BC, CA, AB of triangle ABC at
D, E, F. respectively. The radius of the circle is 4. If BD=8,
DC=6. Find AB and Ac.
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