In Fig. AB is a diameter of the circle, AC =6 | vedclass

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Question

Given, $AC =6\, cm$ and $BC =8 \,cm$

We know that, triangle in a semi-circle with hypotenuse as diameter is right angled triangle.

$	herefore$

Vedclass · Accepted Answer

$54.5$

Vedclass · Answer

Given, $AC =6\, cm$ and $BC =8 \,cm$

We know that, triangle in a semi-circle with hypotenuse as diameter is right angled triangle.

$	herefore$ $\angle C=90^{\circ}$

In right angled $	riangle ACB$, use Pythagoras theorem.

$	herefore$ $A B^{2}=A C^{2}+C B^{2}$

$\Rightarrow$ $A B^{2}=6^{2}+8^{2}=36+64$

$\Rightarrow$ $A B^{2}=100$

$A B=10 \,cm$ [since, side cannot be negative]

$	herefore \quad$ Area of $	riangle A B C=\frac{1}{2} 	imes B C 	imes A C=\frac{1}{2} 	imes 8 	imes 6=24\, cm ^{2}$

Here, diameter of circle, $A B=10 \,cm$

$	herefore$ Radius of circle, $r=\frac{10}{2}=5\, cm$

Area of circle $=\pi r^{2}=3.14 	imes(5)^{2}$

$=3.14 	imes 25=78.5 \, cm ^{2}$

Area of the shaded region $=$ Area of circle $-$ Area of $	riangle ABC$

$=78.5-24=54.5 \, cm ^{2}$

In $Fig.$ $AB$ is a diameter of the circle, $AC =6\, cm$ and $BC =8 \,cm .$ Find the area of the shaded region (Use $\pi=3.14$ ). (in $cm ^{2}$)

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