Two Inradii in a Right Triangle

TrianglesVideo challenge · SAV19

Two Inradii in a Right Triangle

CBSE Class 10 · Solve it one decision at a time. A wrong pick earns a nudge, never the answer.

Step 1 of 8

The problem

In right △ABC\triangle ABC (with ∠B=90∘\angle B = 90^\circ), altitude BD⊥ACBD \perp AC is drawn. The incircle of △ABD\triangle ABD has radius r1=3 cmr_1 = 3\text{ cm}, and the incircle of △CBD\triangle CBD has radius r2=4 cmr_2 = 4\text{ cm}. What is the inradius rr of the full triangle △ABC\triangle ABC?

Step 1 · Your move

Before seeing the step-by-step breakdown, what inradius rr did you find for the full △ABC\triangle ABC?

ABCDr₁ = 3r₂ = 4
Right △ABC\triangle ABC (∠B=90∘\angle B = 90^\circ) · Altitude BD⊥ACBD \perp AC · r1=3 cmr_1 = 3\text{ cm}, r2=4 cmr_2 = 4\text{ cm}
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