Question

Can someone please answer this and explain how you got it? Or just show your work for it please and thank u <3

Answer 1

Answer:

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Step-by-step explanation:

we know, ∠BGA = 90

In right angled triangle BGA

AB = 12 cm (diameter of circle)

⇒ (AB)2 = (AG)2 + (BG)2

⇒ 122 = 82 + (BG)2

⇒ BG = 4√5

In right angled triangle BCG

Let CG be x cm.

⇒ (BC)2 = (CG)2 + (BG)2

⇒ (BC)2 = x2 + (4√5)2 ----(1)

As we know,

⇒ (BC)2 = CG × CA ----(2)

From equation (1) and equation (2)

⇒ x2 + (4√5)2 = x × (x + 8)

⇒ x2 + (4√5)2 = x2 + 8x

⇒ 8x = 80

⇒ x = 10 cm

From equation (2)

⇒ (BC)2 = CG × CA

⇒ (BC)2 = 10 × 18 = 180

⇒ BC = √180 = 6√5

6 × 5 = 30