Question

12. In the figure, ∆APB = 90°. Find the length of
ОP.
​

Answer 1

Answer:

  The length of ОP = $4\sqrt{2}$ units.

Explanation:

• In the figure a circle with centre 'O' and radius 'r' is given. Also there is an external point 'P' from the circle.

∠APB = 90° and radius, r = 4 units.

• We need to find the length of OP.

• Sine function can be defined as the "ratio of the length of the opposite side to that of the hypotenuse in a right angled triangle". The sine function is used to find the unknown angle or sides of a right angled triangle.

• Here in the figure, line OP divides the ∠APB into two equal angles. i.e., ∠APO and ∠OPB.
• Therefore, ∠APO and ∠OPB will be equal to half of ∠APB.

∠APO = ∠OPB = $\frac{90}{2}$ = 45°. Let us consider this as angle Ф.

• Now, consider the triangle ΔOPA. Here, sinФ = $\frac{oppositeSide}{hypotenuse}$

sinФ = $\frac{OA}{OP}$

sin (45°) = $\frac{4}{OP}$, where OA = radius = 4 units.

⇒ $\frac{1}{\sqrt{2} }$ = $\frac{4}{OP}$

∴ OP = $4\sqrt{2}$ units.

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

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Answer 2

Answer:

the correct answer is 4√2 units

Step-by-step explanation:

For explanation open the image

hope it helps you