Question

Triangle ABC is inscribed in a semicircle
AB = 12 cm and BC is 16cm find
AC
and the shaded region.​

Answer 1

Step-by-step explanation:

Solution:-

Given : AB = 12 cm, BC = 16 cm and AB is ⊥ to BC

Now, applying Pythagoras Theorem,

Hypotenuse² = Perpendicular² + Base²

⇒ AC² = AB² + BC²

⇒ AC² = 12² + 16²

⇒ AC² = 144 + 256

⇒ AC² = 400

⇒ AC = √400

AC = 20 cm

There is a relation between Hypotenuse (AC) and Circumradius (r).

The hypotenuse is the diameter of the circle and, and its center is exactly the midpoint of the hypotenuse.

So, Hypotenuse = 2r

Therefore,

r = hypotenuse/2

r = 20/2

Radius of the circle = 10 cm

Answer 2

Answer:

i) 20cm and ii) 61 cm^2

Step-by-step explanation:

AB = 12cm

BC = 16cm

AC = ?

by Pythagoras theorem

i) $(AC)^2 = (AB)^2 + (BC)^2$

$(AC)^2 = (12)^2 + (16)^2$

$(AC)^2$ = 144 + 265

$(AC)^2$ = 400

AC = $\sqrt{400}$

therefore Hypo = diameter = 20cm

Diameter = 2r

20 = 2r

20/2 = r

r = 10cm

ii) Area of shaded region = Area of semi circle - Area of triangle

= $\pi$r^2/2 - 1/2*B*H

= 3.14* 10^2/2 - 1/2*12*16

= 3.14* 100/2 - 1*6*16

= 3.14*50- 96

= 157 - 96

= 61 $cm^2$

THANK YOU!!!