Question

PQ and PR are tangents to circle with Centre O such that QPR=700 then OQR is

Answer 1

Given :  PQ and PR are tangents to circle with Centre O such that  ∠QPR = 70°  

To Find : ∠OQR

Solution:

PQ and PR are tangents to circle with Centre O

=> ∠OQP = 90°

   ∠ORP  = 90°

 

 ∠QPR = 70°

in ΔQPR

PQ = PR   Tangent

=> ∠RQP = ∠QPR

∠RQP + ∠QPR +   ∠QPR = 180°

=> 2 ∠RQP  +  70°  = 180°

=>  2 ∠RQP  = 110°

=> ∠RQP  = 55°

∠OQP = 90°

∠OQP =  ∠OQR + ∠RQP

=> 90° =  ∠OQR +55°

=>  ∠OQR = 35°

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Answer 2

Step-by-step explanation:

Given PQ and PR are tangents to circle with Centre O such that QPR=70 degree then OQR is

• Angle QOR = 2 x angle QPR
•                    = 2 x 70
•                   = 140 degrees
• Since both are radii we have OQ = OR
• So OQR is an isosceles triangle.
• Let OQR = ORQ = m
• Since the sum of all the angles of the triangle OQR is 180 degree we get
• So m + m + 140 = 180
•    2m + 140 = 180
•    2m = 180 – 140
•    2m = 40
•    Or m = 40 / 2
•    Or m = 20 degree
•     So OQR = 20 degree

Reference link will be

https://brainly.in/question/2715287