Question

Two circles touch each other externally at the point C. If common tangent
to the two circles touches the circles at the point A and B respectively,
then the measure of angle ACB is-
​

Answer 1

Answer:

90°

Step-by-step explanation:

∠acb + ∠abc + ∠bac = 180°   [sum of the interior angles in a triangle]

α + β + (α + β) = 180°

2α + 2β = 180°

α + β = 90°

∴ ∠ACB = α + β = 90

Answer 2

Answer:

ZAPC = a

ZPAC = a

ZPBC = B

ZBPC В

In ZABP

a + B+ a + B = 180

2(a + b) = 180

a + B = 90

ZAPB = a + B = 90.