Question

Find the area of an isosceles triangle with equal sides are 10cm and inscribed by a circle of radius 10cm?

Answer 1

Let the isosceles triangle be ABC.

AB=AC=10cm

OB=OC=OA=10cm (radius of circle)

Angle ADC = 90° (altitude)

Let OD = x

To find:-

Area of triangle

Solution:-

In ∆ODC, applying Pythagoras theorem,

OC2=OD²+CD²

CD2=(10)²−x² … (1)

In ∆ADC, applying Pythagoras theorem,

AC2=AD²+CD²

100=(10−x)²+(100−x²) … (from (1))

100=100+x²−20x+100−x²

20x=100

x=5cm

Now, as we have the value of x, calculate the value of CD and AD:-

For CD:-

CD2=(100−x²)=(100−25)=75cm

CD=√75=5√3cm

For AD:-

AD=10−x=10–5=5cm

We know that, to calculate the area of the triangle we need:-

Base - 2 × CD = 10√3cm

Height- AD = 5cm

Area = 1/2 × base × height

Area = 1/2 × 10√3 × 5cm²

Area = 86.6/2cm2

Area = 43.3cm2

Therefore, the area of an Isosceles Triangle is 43.3 cm2.

Find image attached.