Question

Two circles intersect each other in point a and b one tangent Touches the circlesin point P and q. Line AB intersects tangent pq in point C. Complete the following activity to prove that c is mid point of seg PQ​

Answer 1

Answer:

Now, ∠APQ=∠ABP ....(1) since angle in the alternate segment are equal.

Now, ∠AQP=∠ABQ ....(2) since angle in the alternate segment are equal.

In △PAQ,

∠PAQ+∠APQ+∠AQP=180

∘

by angle sum property

⇒∠PAQ+(∠ABP+∠ABQ)=180

∘

from (1) and (2)

⇒∠PAQ+∠PBQ=180

∘

Hence proved.