Question

5. In the following figure, AD is a straight line.
OP I AD and O is the centre of both the circles.
If OA= 34 cm, OB = 20 cm and OP=16 cm; find
the length of AB.
O
Р
D
А
B
с

please give me answer​

Answer 1

Answer:

Step-by-step explanation:

For the inner circle, BC is a chord and OP is perpendicular to BC

We know that the perpendicular to a chord, from the centre of a circle, bisects the chord.

∴BP=PC  

By Pythagoras theorem,

OA^ 2

=OP^  2 +BP^  2

 ⇒BP  ^2 =20^  2 −16 ^ 2 =400−256=144

∴BP=12cm

For the outer circle,AD is the chord and OP is perpendicular to AD

We know that the perpendicular to a chord, from the centre of a circle, bisects the chord.

∴AP=PD

By Pythagoras theorem,

OA^  2 =OP^  2  +AP  ^2

⇒AP^  2 =34^  2 −16^ 2  

=1,156‬−256=900

⇒AP=30cm

AB=AP−BP =30−12 =18cm