Question

Two circles intersect each other at points a and b with a common tangent touching them at c andd.find cad+cbd

Answer 1

the answer is 180°
refer to the image attached for solution

Answer 2

Answer:

Step-by-step explanation:

We are given that two circles intersect each other at points a and b with the common tangent cd touching both the circles.

Then, angle made by the chord and the tangent= angle in alternate segment, that is ∠ADC=∠ABD and ∠ACD=∠ABC.

Now, as ∠ABD+∠ABC=∠ADC+∠ACD

⇒∠CBD=180°-∠CAD (because it is clear from the figure that∠ABD+∠ABC=∠CBD)

⇒∠CAD+∠CBD=180°

Hence, ∠CAD+∠CBD=180°