Question

if tangent pa and pb from a point p to a circle o are inclined to each other at angle of 80 then angle POA is equal to _​

Answer 1

Answer:

angle POA Is equal to 50°

are a Chaitanya student

Answer 2

Given /_P = 80°

On observing we find that ; ∆POA is congruent to ∆POB { SSS CRITERIA }

• PO = PO ( SAME SIDE)
• OA = OB ( RADII OF SAME CIRCLE )
• PA = PB ( TANGENTS FROM A COMMON POINT ARE EQUAL)

Thus by cpct ; /_APO = /_BPO = 1/2 ( /_P)

• /_APO = 1/2 × 80°
• /_APO = 40°

/_OAP = 90°

(AS RADIUS IS PERPENDICULAR TO TANGENT AT THE POINT OF CONTACT)

Thus in ∆PAO ; by angle sum property;

• 90° + 40° + /_POA = 180°
• /_POA = 50°

#answerwithquality

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