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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?
Answer & Solution
Correct answer: B.
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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