Multiple choice

PA is a tangent from an external point P to a circle with centre O. If ?POB =1150 , find ?APO. (where AB is diameter)

  1. 300

  2. 350

  3. 250

  4. 200
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

AB is diameter, so ∠ABO = 90° (angle in semicircle). In ΔAOB, ∠AOB = 115° (given as POB, same angle), so ∠OAB = 180° - 90° - 115° = 25°. PA is tangent, so ∠OAP = 90° (radius ⟂ tangent). In ΔOAP, ∠APO = 180° - 90° - 65° = 25°. The key is recognizing tangent-radius perpendicularity and angle in semicircle property.

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