Question

In the figure angle APB 90 degree find the length of OP

Answer 1

Step-by-step explanation:

Answer in attachment

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Answer 2

Concept:

We need to know how to solve sin∅

$Sin\theta=\frac{opposite}{hypotenuse}$

Given:

We are given an external point P from circle with center O and radius R.

∠APB=90°

To find :

We need to find of length of OP.

Solution:

Now, in ΔOPA

$Sin\theta=\frac{OA}{OP}$

$\theta$=∠OPA=$\frac{\angle BPA}{2}$=45°

⇒∠∠∠

⇒$Sin45^{\circ}=\frac{4}{OP}$

⇒$\frac{1}{\sqrt{2} } =\frac{4}{OP}$

⇒$OP=4\sqrt{2}$

Therefore, length of OP is $4\sqrt{2}$