Question

In the figure, two circles intersect each other
at points A and B. Line PQ is the common
tangent touching the circle in points P and Q
as shown. Prove that LPAQ +_ PBQ = 180°.​

Answer 1

Answer:

Two circles intersect each other at points A and B. their common tangent touches the circles at points P and Q as shown in the figure. Show that the angles PAQ and PBQ are supplementary.

Step-by-step explanation:

Refer to the attached file.

Answer 2

Answer:

Join AB. PQ is the tangent and AB is a chord

Thus angle QPA = angle PBA (angles in alternate segment)

Similarly,

Angle PQA = angle QBA

Hence,

Angle QPA + Angle PQA = Angle PBA + Angle QBA

But in Triangle PAQ

Angle QPA + Angle PQA = 180 degree - Angle PAQ

And Angle PBA + Angle QBA = Angle PBQ

Thus,

Angle PBQ = 180 - Angle PAQ

Angle PBQ + Angle PBQ = 180 degree

Thus, PROVEN

PLZ FOLLOW ME