Question

In the given figure, O is centre of the circle. Find the value of x and y? ​

Answer 1

Answer:

• The value of x=30cm and y = 18cm.

Step-by-step explanation:

P is the exterior point to the circle with centre O

Radius = 5cm

Length of the tangent = 12 cm

Distance between the point and centre of the circle = x cm

We know that

The angle between the radius of the circle and the tangent at the point of contact is 90°

By Pythagoras Theorem

Hypotenuse² = Side²+Side²

⇛OP² = OT1² +PT1²

⇛x² = 24²+18²

⇛x² = 576+324

⇛x² = 900

⇛x² = 30²

⇛x = √(30)²

⇛x = √(30*30)

⇛x = 30cm

We know that

The lengths of tangents drawn from the exterior point to the circle are equal.

PT1 = PT2

y = 18 cm

Answer: Hence, the value of x=30cm and y = 18cm.

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Answer 2

Answer:

x=30 cm

y=24 cm

Step-by-step explanation:

y=24 cm

x=√(24²+18²)=√[6²(4²+3²)]=6√(16+9)=6√25=6×5=30 cm