If PQ and PR are tangents to a circle with centre 'O' from an external point P, then sum of ∠ PQO and ∠ PRO is____.
A
90∘
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B
180∘
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C
270∘
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D
can't be determined.
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Solution
The correct option is B180∘ Join centre 'O' with 'Q' and 'O' with 'R' as shown in figure.
By Theorem- Tangents at any point to a circle is perpendicular to the radius through the point of contact. ∵ OQ is radius and PQ is a tangent and OR is radius and PR is a tangent. ∴ OQ ⊥ PQ and OR ⊥ PR. ⇒∠ PQO = 90∘ and ∠ PRO = 90∘. Hence, ∠ PQO + ∠ PRO = 180∘.