Q. 294.4( 18 Votes )

Equal circles wit

Answer :

We know that ∠ADO’ = 90° (since O’D is perpendicular to AC)

As we know radius is perpendicular to the tangent.

So, OC ⊥ AC

⇒ ∠ACO = 90°

In ΔADO’ and ΔACO,

∠ADO’ = ∠ACO (each 90°)

∠DAO = ∠CAO (common)

By AA criteria,

ΔADO’ ∼ ΔACO

As we know corresponding sides of a triangle are in ratio.

AO = AO’ + O’X + OX

As radii of two circles are equal.

⇒ AO = AO’ + AO’ + AO’

= 3 AO’




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