Height of a Triangle With Inscibed Circle Given Base and Radius of Circle
Suppose we have an isosceles triangle with base given, and a circle inscribed inside it, of given radius.
![](/igcse-maths/circle-in-isosceles-triangle-1.png)
We can calculate the height of the triangle.,
Label the Vertices of the triangle A, B and C and draw a line from the centre of the circle to B. The angle \[x= tan^{-1}(8/10)=38.66 \deg\]
.
![](/igcse-maths/circle-in-isosceles-triangle-2.png)
Draw a line from the centre of the circle to the side AB, which meets the side at P.
![](/igcse-maths/circle-in-isosceles-triangle-3.png)
The two triangles so far construct, have the side OB in common, correspond equal side, equal to the radius of the circle, and corresponding equal angles (right angles), so angle \[APO=x\]
and angle \[ABC=2x= 77.32 \deg\]
.
Now construct another right angled triangle as shown.
![](/igcse-maths/circle-in-isosceles-triangle-4.png)
The height of the triangle is then \[AQ tan (2x)=44.44 cm\]
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