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Circles
NCERT Exemplar
CBSE
Grade 10
Question:
If $TP$ and $TQ$ are two tangents to a circle with center $O$ so that $\angle POQ = 110^\circ$, then $\angle PTQ$ is equal to:
(a) $60^\circ$
(b) $70^\circ$
(c) $80^\circ$
(d) $90^\circ$
(a) $60^\circ$
(b) $70^\circ$
(c) $80^\circ$
(d) $90^\circ$
Step-by-Step Solution
Key Concept: In quadrilateral $OPTQ$, $\angle OPT = \angle OQT = 90^\circ \Rightarrow \angle PTQ + \angle POQ = 180^\circ$.
$\angle PTQ = 180^\circ - \angle POQ = 180^\circ - 110^\circ = 70^\circ$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Calculating $\angle PTQ = 180^\circ - 110^\circ = 70^\circ$: 1.0 Mark
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🎯 Official CBSE Marking Scheme:
Calculating $\angle PTQ = 180^\circ - 110^\circ = 70^\circ$: 1.0 Mark
Correct Answer: $70^\circ$
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