Question

AB is a diameter of a circle of radius 10 and centre o.
A tangent is drawn from B to a circle of radius
8 and centre o which touches a circle of to radius 8
and Centre o at Point D. Ray BD Interest to
a circle of radius 10 and centre o at Point c find AC ​

Answer 1

AC = 16

Step-by-step explanation:

See the attached diagram.

Here, ∠ ACB will be 90° as AB is the diameter and C is a point on the circumference of the large circle with radius 10.

Now, BC ⊥ OD as BC is a tangent to the smaller circle with radius 8.

So, triangles Δ ABC and Δ OBD are similar triangles as OD ║ AC and they both are perpendicular to the line BC.

Then, $\frac{AC}{AB} = \frac{OD}{OB}$

⇒ $AC = \frac{8}{10}\times 20 = 16$ (Answer)

{Since AB = 2 × OB = 2 × 10 = 20}

Answer 2

Answer:

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Step-by-step explanation: