Question

A right angled triangle of sides containing right angle are 6cm and 8cm is circumscribed in a circle with centre O of radius 5cm as shown in figure. Find the area of the shaded region​

Answer 1

† Question †

• A right angled triangle of sides containing right angle are 6cm and 8cm is circumscribed in a circle with centre O of radius 5cm as shown in figure. Find the area of the shaded region

$\rule{300}2$

【 Solution 】

→∆ ABC is a rights angle triangle.

*By Pythagoras theorem,

$\rightarrow AB=\sqrt{6^2+8^2}\\\rightarrow AB=\sqrt{36+64}\\\rightarrow AB=\sqrt{100}\\\rightarrow AB=10cm$

• AB is also the diameter of the circle.

→Diameter = 10cm

→Radius = 5cm

→Area of the shaded region = Area of - Area of triangle

$\rightarrow πr^2-\frac{1}{2}×base×height \\\rightarrow3.14-\frac{1}{2}×8×6\\\rightarrow78.5-24\\\rightarrow54.5cm^{2}$