Question

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Answer 1

Answer:

If the radius of the circle is 6 cm and AG = 8, then the length of BC is 13.4 cm.

Step-by-step explanation:

Referring to the figure attached below

The radius of the circle, AO = 6 cm

∴ The diameter of the circle, AB = 6*2 = 12 cm

AG = 8 cm

Join points B and G.

Step 1:

We know that the angle subtended by the diameter of the circle on any point of the circle is 90°.

∴ ∠AGB = 90°

Let’s assume ∠GAB = “θ”.

Applying the trigonometry properties of triangles in ∆AGB, we get

cos θ = Base/ hypotenuse=AG/AB

⇒ cos θ = 8/12

⇒ cos θ = 2/3

⇒ θ = cos⁻¹ (0.667)

⇒ θ = 48.16°

Step 2:

We also know that the angle made by the tangent and the radius of the circle is equal to 90°.

∴ ∠BCO = ∠BCA = 90°

Now, consider ∆ABC and apply the trigonometry properties of triangles, we get

tan θ = perpendicular/base= BC/AB

⇒ tan 48.16° = …… [here ∠GAB = ∠CAB = θ = 48.16°]

⇒ BC = 1.116 * 12

⇒ BC = 13.39 cm ≈ 13.4 cm

Thus, the length of BC is 13.4 cm .

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