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In the configuration OACB above, what does this imply for the sum of the remaining angles, namely angle AOB plus angle ACB?
ATheir sum equals 90 degrees
BTheir sum equals 180 degrees
CTheir sum equals 270 degrees
DTheir sum equals 360 degrees
Answer & Solution
Correct answer: B. Their sum equals 180 degrees
1. The angle sum of any quadrilateral equals 360°.
2. In OACB the angles at A and B already account for 90° + 90° = 180°.
3. The remaining two angles, angle AOB and angle ACB, must therefore sum to 360° − 180° = 180°.
4. Equivalently, the angles between the radii and the angle between the tangents are supplementary.
5. So the supplement relation holds for every pair of tangents from an external point.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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