Question

In figure, O is the center of circle and PA is the tangent. If BC = 3cm, AC = 4cm and angle BAC = angle OPA ,find OP.​

Answer 1

Answer:

Consider the problem

∠ACB is an angle in a semi circle

Therefore, ∠ACB =90

∘

Now, in ΔACB

we use Pythagoras Theorem (AB)

2

=(AC)

2

+(BC)

2

∴AB

2

=16+9

AB=

25

=5cm

So,

Radius OA=

2

1

AB

OA=

2

1

×5

=

2

5

cm

Now, since ΔACB∼ΔPAO

CA

BA

=

AP

OP

Therefore,

AP

OP

=

4

5

Step-by-step explanation:

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