A geometry problem by Ashley Shamidha
Geometry
Level
3
Triangle ABC is a right angled triangle. Given , if a circle is the incentre of the triangle, i.e touch all three sides internally, then find the area of this circle.
The answer is 12.56.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
BC = √(6^2+8^2) = 10 cm | Let the circle meet AB at D, BC at E and AC at F | OD = OE = OF = r (radius of circle) | Area ∆ABC = Area of (∆OAB + ∆OBC +∆OAC) | 1/2 × 6 × 8 = 1/2×r×6 + 1/2×r×8 +1/2×r×10 | 24 = r/2 ( 6+8+10) | r/2 = 1 Therefore r = 2cm | Area of circle = πr^2 = 22/7 × 2 × 2 = 12.56cm^2