Question

Q.7: In the figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

Q.8: Area of the largest triangle that can be inscribed in a semi-circle of radius r units is

(A) r² sq. units (B) ½ r² sq. units

(C) 2 r² sq. units (D) √2 r² sq. units
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Answer 1

$\large \{\purple{\underline{\underline{ \boxed{Solution 01}}}}$

Given:

• Radius (r1) of larger circle = 7 cm
• Radius (r2) of smaller circle = $\tt \: \frac{7}{2} cm$

Area of smaller circle =

$\tt \: πr {}^{2} \\ \\ \tt \:= \frac{22}{7} × \frac{7}{2} \times \frac{7}{2} \\ \\ \tt \: =772cm {}^{2}$

Area of semi-circle AECFB of larger circle  = 

$\tt \: = \frac{1}{2} \times \frac{22}{7} ×(7)2 \\ \\ \tt \: = 77 cm {}^{2}$

Area of ΔABC = 

$\tt \: 12×AB×OC \\ \tt \:=12×14×7=49cm {}^{2}$

Area of the shaded region

= Area of smaller circle + Area of semi-circle AECFB − Area of ΔABC

$\tt \: =772+77-49 \\ \tt \: =28+772 \\ \tt \: =28+38.5=66.5cm {}^{2}$

$\large \{\purple{\underline{\underline{ \boxed{Solution 02}}}}$

$\\ \tt \: A \: semicircle \: has \: the \: largest \: triangle's \: base \: as \: its \: diameter,\\ \tt \ and \: its \: perpendicular \: or \: height \: as \: its \: radius \: \\ \tt \: \frac{1}{2} \times 2r \times r = r^{2}$

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$\sf \: @WildCat7083$