Question

Question 1
In the following figure, AD is a straight line, OP 1 AD and is the centre of both the
circles. If OA - 34cm, OB = 20 cm and OP = 16 cm; find the length of AB.
C
D​

Answer 1

Answer:

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Answer 2

answer is 18 cm

Step-by-step explanation:

ANSWER:-

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