The Inradius of a Right Triangle

Circles

The Inradius of 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 4

The problem

A circle with centre

O

and radius

r

is inscribed in

\triangle ABC

with

\angle C = 90^\circ.

It touches

BC,

CA

and

AB

at

D,

E

and

F.

If

BC = a,

CA = b

and

AB = c,

prove that

r = \dfrac{a + b - c}{2}.

Step 1 · Your move

Why is $OD \perp BC$ and $OE \perp CA$ ?

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