Question

two circle intersect each other at C and D line ab is the common tangent prove that angle ACB + angle ADB is equal to 180 degree...plz answer me fast

Answer 1

Answer:

Step-by-step explanation:

WE are given that the two circles intersect each other at C and D and the line ab is the common tangent, then

Angle made by the chord and tangent= angle in alternate segment,

therefore ∠CBA=∠CDB and ∠CAB=∠CDA.

Now, as ∠CDB+∠CDA=∠CBA+∠CAB

⇒∠ADB=180°-∠ACB ( because from the figure it is given that ∠CDB+∠CDA=∠ADB)

⇒∠ADB+∠ACB=180°

Hence proved.

Answer 2

Answer:

The above result is proved with the help of tangent chord theorem and explained below.

Step-by-step explanation:

Given two circle intersect each other at C and D line AB is the common tangent. we have to prove that angle ACB + angle ADB is equal to 180 degree.

we know that sum of all angles of triangle is equal to 180°

∴ In triangle ADB

∠DAB+∠ADB+∠ABD=180°

⇒ ∠3 + ∠2 + ∠4 = 180°  →  (1)

Now, by tangent chord theorem which states that

The angle formed between a chord and a tangent through one of the end points of tangent and chord in any circle is equal to the angle formed by the chord in the reverse side of the previous angle.

⇒ ∠3=∠5 and ∠4=∠6

eq (1) becomes ∠5 + ∠2 + ∠6 = 180

                          ⇒ ∠1  + ∠2 = 180°

Hence,  ∠ACB + ∠ADB = 180