Question: 3 - If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to
Answer: (a) 50°
Explanation: Here; `∠APB = 80°`
`∠OPA = ½ xx ∠APB`
`= ½ xx 80^o = 40^o`
`∠OPA + ∠OAP + ∠POA = 180°`
Or, `40° + 90° + ∠POA = 180°`
Or, `∠POA = 180° - 130° = 50°`
Question: 4 - Prove that the tangents drawn at the ends of a diameter are parallel.
Answer: Construction: Draw a circle with centre O. Draw a diameter AB. Draw tangents MN and OP which respectively touch A and B.
To Prove: MN || OP
`∠MAB = ∠PBA = 90°` (since radius is perpendicular to tangent
Since alternate angles are equal
Hence; MN || OP proved
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