A poor artist on the street makes funny cartoons for children and earn

1.	A poor artist on the street makes funny cartoons for children and earns his living, Once he made a comicface by drawing a circle within a cirele, the radius of the bigger circle being 30 cm and that of smallerbeing 20 cm as shown in the ligure. What is the area of the cap given in this figure? What qualities ofthis artist are being reflected here?30-2
Answer» Radius of bigger triangle is with centre O=30 cm Radius from O'=20cm difference of their radii =distance between their centres O andO' =10cm AB is a tangent if smaller circle so,/_OCA=90°=/_OCB In triangle ica AO²=AC²+CO² 30²=AC²+10² 900=AC²+100 AC=20√2 AC=CB AB=AC+CB AB=AC+CB AB=2AC AB=2*20√2 AB=40√2cm CD=30-10 =20cm Area of cap=AR of adb 1/2×AB×CD 1/2×40√2×20=400√2cm² 400×1.414 =565.6cm²

A poor artist on the street makes funny cartoons for children and earns his living, Once he made a comicface by drawing a circle within a cirele, the radius of the bigger circle being 30 cm and that of smallerbeing 20 cm as shown in the ligure. What is the area of the cap given in this figure? What qualities ofthis artist are being reflected here?30-2

Answer»

Radius of bigger triangle is with centre O=30 cm

Radius from O'=20cm

difference of their radii =distance between their centres O andO' =10cm

AB is a tangent if smaller circle so,/_OCA=90°=/_OCB

In triangle ica

AO²=AC²+CO²

30²=AC²+10²

900=AC²+100

AC=20√2

AC=CB

AB=AC+CB

AB=2AC

AB=2*20√2

AB=40√2cm

CD=30-10

=20cm

Area of cap=AR of adb

1/2×AB×CD

1/2×40√2×20=400√2cm²

400×1.414

=565.6cm²