Two circles touch each other externally at C and AB is common tangent of circles, then is

Question

Two circles touch each other externally at C and AB is common tangent of circles, then $∠ A C B$ is

Smart Achievers · Accepted Answer

(4)

Draw CM perpendicular to AB.

Now, AM = MC and MB = MC (tangents drawn from external point are equal).

⇒ AM = MC

⇒ $∠ M A C$ = $∠ M C A$ = 45°

(Since Δ AMC is right triangle)

∴ Also, MB = MC ⇒ $∠ M B C$ = $∠ M C B$ = 45° (Since Δ MBC is right angle triangle)

∴ $∠ A C B$ = $∠ M C A$ + $∠ M C B$ = 45° + 45° = 90° ⇒ $∠ A C B$ = 90°

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