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Question:

In ΔABC, m∠B=90°, AB=4 and BC=3, then the radius of circle touching all three vertices of a triangle will be:

2

3

2.5

3.5

Solution:

In ΔABC, m∠B=90°, AB=4, BC=3
By Pythagoras theorem, AC²=AB²+BC²=(4)²+(3)²=25
∴AC=5
Then the radius of a circle touching all the three sides of triangle ABC = AC/2 = 5/2 = 2.5