Question

Help me please find the circumference of D pls

Answer 1

`\huge\underline\color{skyblue}{Answer ☘}`

( Note~ refer the attachment for naming of certain points )

Now given that ,

AB = 12 cm

BC = 8 cm

We know that , angle in a semicircle = 90°

`\purple{Therefore \:, triangle\: ABC\: is \:a \:right \:- \:angled\: traingle.}`

Now in right angled triangle ABC ,

`\purple{by \:Pythagoras \:theorem}`

`H {}^(2) = P {}^(2) + B {}^(2) \\ AC {}^(2) = AB {}^(2) + BC {}^(2) \\ AC {}^(2) = 12 {}^(2) + 8 {}^(2) \\ AC {}^(2) = 144 + 64 \\ AC {}^(2) = 208 \\ AC = √(208) = 14.42cm (approx.)`

Now , AC is the diameter of the circle and also the hypotenuse of the given right angled triangle.

And ,

`\pink{AC = diameter\: of \:circle = 14.42 cm}`

`\blue{Therefore \: , radius = (diameter)/(2) }\\`

`\pink{radius = 7.21 cm}` ( approx. )

hope helpful~