Question

10. In a circle of radius 5 cm, AB and
AC are two chords such that
AB= AC = 8 cm. What is the length of
chord BC?
1)​

Answer 1

Answer:

Again, the internal bisector of an angle divides the opposite sides in the ratio of the sides containing the angle.

P divides BC in the ratio 6:6=1:1.

P is mid-point of BC.

OP ⊥ BC.

In △ ABP, by pythagoras theorem,

AB

2

=AP

2

+BP

2

BP

2

=36−AP

2

....(1)

In △ OBP, we have

OB

2

=OP

2

+BP

2

5

2

=(5−AP)

2

+BP

2

BP

2

=25−(5−AP)

2

.....(2)

From 1 & 2, we get,

36−AP

2

=25−(5−AP)

2

36=10AP

AP=3.6cm

Substitute in equation 1,

BP

2

=36−(3.6)

2

=23.04

BP=4.8cm

BC=2×4.8=9.6cm