Given figure $TP$ and $TS$ are tangents to the given circle

Question

In the given figure $TP$ and $TS$ are tangents to the given circle $r$ is point of circumference

im trying but i could't find any idea and i forget my geometry knowledge please can some help this problem

thank you so much

1,2,3 represent equal angles? – rhombicosicodecahedron May 01 '19 at 08:28 — rhombicosicodecahedron, May 01 '19 at 08:28
@rhombicosicodecahedron.. i dont know xtacly sir – SURYA May 01 '19 at 08:35 — SURYA, May 01 '19 at 08:35

score 0 · Answer 1 · edited Jun 12 '20 at 10:38

0

$\angle PRS = \angle TPS $ by inscribed angle theorem

$\angle TPS = \angle TQP$ by your definition of $Q$

So, we have $\angle PRS = \angle TQP$ and that means that $TQ||SR$ (corresponding angles)

To prove 7.2 note that $\angle TSP = \angle TPS = \angle TQP$ and so TPQS is inscribed (it is equivalent to $\angle TSP = \angle TQP$)

To prove 7.3 note that we know that TPQS is inscribed, so $\angle TPS = \angle TQS$ (by inscribed angle theorem)

edited Jun 12 '20 at 10:38

Community

answered May 01 '19 at 08:37

kvardekkvar

1 Answers1