Q. 414.4( 5 Votes )

In Fig. 10.101, P

Answer :

Given:


QPR = 46°


Property 1: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.


Property 2: Sum of all angles of a quadrilateral = 360°.


By property 1, ∆OQP is right-angled at OQP (i.e., OQP = 90°) and ORP is right-angled at ORP (i.e., ORP = 90°).


Now by property 2,


OQP + ORP + QOR + QPR = 360°


QOR = 360° - (OQP + ORP + QPR)


ROP = 360° - (90° + 90° + 46°)


ROP = 360° - 226°


ROP = 134°


Hence, ROP = 134°

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