Q. 11 A24.2( 5 Votes )

# Two circles touch each other externally at the point C. A direct common tangent AB touch the two circle at the points A and B. Value of ∠ACB isA. 60°B. 45°C. 30°D. 90°

Let D be the point where the transverse tangent meets the direct tangent

DAC = DCA (Tangents drawn from an external point to the same circle are always equal and hence Δ DAC is isosceles)

Let DAC = DCA = a …Equation(i)

DBC = DCB (Tangents drawn from an external point to the same circle are always equal and hence Δ DBC is isosceles)

Let DBC = DBA = b …Equation(ii)

From Δ ABC we get

ACB = 1800-(a + b)

From Equation (i) and (ii) we get

DCA + DCB = (a + b)

ACB = (a + b)

Equating ACB found in the above two cases we get

1800-(a + b) = (a + b)

(a + b) = 900

So ACB = 900

So D is the correct option

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