Question

Two circles touch externally at A. Secants PAQ and RAS intersect the circles at P, Q, R and S. Tangent are drawn at P, Q , R ,S. Show that the figure formed by these tangents is a parallelogram.

Answer 1

Please mark me as brainliest

Answer 2

The figure formed by tangents is a parallelogram ABCD.

Total number of secants = 2 = PAQ and RAS

On, joining the tangents -

In ΔMPT and ΔNQT  

∠MPT = ∠MTP

∠NTQ = ∠NQT

Thus, MP || NQ

As MP is perpendicular to AD, and NQ is perpendiculat to BC,  

Thus, AD || BC,  

Similarly, MR || NS

MRis perpendicular to AB and NS is Perpendicular to CD,  

Thus, AB || CD,

Since all the sides are parallel, thus ABCD is a parallelogram.