In the given figure, ABC is a right-angled triangle with AB=7 cm and AC=9 cm. A circle with center O has been inscribed inside the triangle. Calculate the value of r, the radius of the inscribed circle.
Answer:
2.3 cm
- Let us join O to A,B, and C and draw OD⊥AB, OE⊥BC and OF⊥CA.
We see that OD,OE, and OF are the radius of the circle with center O.
⟹OD=OE=OF=r cm
Also, △ABC is a right-angled triangle. - Let us now find the area of in terms of .
- Comparing the area of obtained in step 1 and step 2, we have
- Applying Pythagoras theorem in , we have
- Now, substituting the value of in , we have
- Hence, the radius of the inscribed circle is .