Question

in each case of the following figures was the centre of the circle find the values of X and Y​

Answer 1

Answer:

In the second diagram:x=y=12cm.

This can be done by using "Pythagoras Theorem"

But I don't know in first diagram.

In first diagram x=5cm.

And y=√55(approximately)

Step-by-step explanation:

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Answer 2

$\large{\bf{\red{Solution\:(i)}}}$

Refer to the 1st attachment for figure (i)

∵radius is always perpendicular to tangent

∴ ∠ OBC = 90°

By pythagoras theorem in Δ OBC

x² = 3² + 4²

x² = 9 + 16

x = √25

$\boxed{\bf{x=5\:cm}}$

∵ AB is a diameter

∴ AB = 2 (OB)=2(4) = 8 cm

By pythagoras in Δ ABC

y² = 3² + 8²

y² = 9 + 64

$\boxed{\bf{y=\sqrt{73\:}cm}}$

$\large{\bf{\red{Solution(ii)}}}$

Refer to the 2nd attachment for figure (ii)

In Δ OBC

by pythagoras theorem

15² = 9² + x²

x² = 225 - 81

x² = 144

$\boxed{\bf{x=12 \:cm}}$

since, tangents drawn from same point to a circle are equal

therefore,

x = y

hence,

$\boxed{\bf{y=12\:cm}}$