Mathematics
In the adjoining diagram, O is the center of the circle and PT is a tangent. The value of x is :
20°
40°
55°
70°
Circles
ICSE Sp 2025
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Answer
From figure,
⇒ ∠QOT + ∠TOP = 180° (Linear Pair)
⇒ 110° + ∠TOP = 180°
⇒ ∠TOP = 180° - 110° = 70°.
⇒ ∠OPT = 90° (Tangent is perpendicular to radius at point of intersection)
In △ TOP,
⇒ ∠OPT + ∠TOP + ∠PTO = 180°
⇒ 90° + 70° + x°= 180°
⇒ x° + 160° = 180°
⇒ x° = 180° - 160° = 20°.
Hence, Option 1 is the correct option.
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