Answer:
The radius of circle is 5 cm
Step-by-step explanation:
Given a right triangle △ABC with right angle C is inscribed in a circle in which
m∠C = 90°, AC = 8 cm, BC = 6 cm
we have to find the radius of circle.
As ACB is right angles triangle where angle C is right angle.
⇒ side AB must be the diameter of circle as angle made at semi circle is 90°
[tex]Radius=AO=\frac{1}{2}AB[/tex]
By Pythagoras theorem
[tex]AB^2=AC^2+CB^2[/tex]
[tex]AB^2=8^2+6^2=64+36=100[/tex]
[tex]AB=10cm[/tex]
[tex]Radius=AO=\frac{1}{2}AB=\frac{1}{2}\times 10=5cm[/tex]
Hence, the radius of circle is 5 cm
