Q. 2 5.0( 3 Votes )

In figure 1, O is the center of a circle, PQ is a chord and PT is the tangent at P. If POQ = 70°, then calculate TPQ. (All India 2011)

Answer :

Given: PT is the tangent at P.


POQ = 70°


Since OP and OQ are the radii of the circle, therefore POQ forms an isosceles triangle.


Therefore, OPQ and PQO are of the same measure.


Let OPQ = 1 and PQO = 2. Thus 1 = 2 ( = x, say)


As sum of all angles of a triangle is 180°, therefore,


OPQ + PQO + POQ = 180°


x + x + 70° = 180°


2x = 110°


x = 55°


Now, PT is tangent at P, therefore TPO = 90°


But, TPO = TPQ + QPO


TPQ = TPO - QPO


= 90° - 55°


= 35°


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