Q. 25.0( 3 Votes )

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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