Question

ln the given fig PQ is a chord and PT is the tangent at P angle POR = 70 digree and find it o is the centre​

Answer 1

Answer:

∠TPQ = 35°

Step-by- step explanation:

For better understanding of the solution, see the attached figure of the problem :

Since, OP and OQ both are radius of same circle

⇒ OP = OQ

Therefore, ΔOPQ is an isosceles triangle since two sides are equal

Now, by using property of isosceles triangle that the corresponding angles to equal sides in an isosceles triangle are equal. We get,  

∠OPQ = ∠OQP  

By using Angle sum property of triangle in ΔOPQ :  

∠POQ + ∠OPQ + ∠OQP = 180°  

⇒ 70° + 2∠OPQ = 180°  

⇒ 2∠OPQ = 110°

⇒ ∠OPQ = 55°

Now, tangent makes right angles with the point of contact with the circle.

⇒ ∠OPT = 90°

⇒ ∠OPQ + ∠TPQ = 90°

⇒ 55° + ∠TPQ = 90°

⇒ ∠TPQ = 35°