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Question

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 B 180
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.


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