if PA and PB are tangents from an outside point P such that angle APB=70' then find angle AOP
Answers
Given : PA and PB are tangents from an outside point P such that angle APB=70°
To find : angle AOP
Solution:
PA and PB are tangents
=> ∠OPA = ∠OPB = 90°
∠APB = 70° Given
∠OPA + ∠OPB + ∠APB + ∠AOB = 360° ( sum of angles of Quadrilateral)
=> ∠AOB = 110°
in ΔOAP and ΔOBP
OA = OB = Radius
OP = OP common
PA = PB Equal tangents
=> ΔOAP ≅ ΔOBP
=> ∠AOP = ∠BOP
∠AOP +∠BOP = ∠AOB = 110°
=> ∠AOP = 55°
Learn More:
The angle between a pair of tangents drawn from a point P to the ...
brainly.in/question/9606826
A(2, 4) and B(5, 8), find the equation ofthe locus of point P such ...
brainly.in/question/13789388
Answer:
PA and PB are tangents
=> ∠OPA = ∠OPB = 90°
∠APB = 70° Given
∠OPA + ∠OPB + ∠APB + ∠AOB = 360° ( sum of angles of Quadrilateral)
=> ∠AOB = 110°
in ΔOAP and ΔOBP
OA = OB = Radius
OP = OP common
PA = PB Equal tangents
=> ΔOAP ≅ ΔOBP
=> ∠AOP = ∠BOP
∠AOP +∠BOP = ∠AOB = 110°
=> ∠AOP = 55°
Step-by-step explanation: