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The picture shows two tangents to a circle from an external point and the radii to the points of contact. The line joining the external point to the centre acts as the perpendicular bisector of:
AThe major arc between the two contact points
BThe chord joining the two points of contact
CEach tangent at the external point only
DThe diameter perpendicular to one of the tangents
Answer & Solution
Correct answer: B. The chord joining the two points of contact
1. The tangent lengths from the external point are equal and the radii to the contact points are equal.
2. The line joining the centre to the external point is the symmetry axis of the kite formed.
3. By that symmetry, the line is the perpendicular bisector of the chord of contact joining the two tangent points.
4. It is not the bisector of an arc or of either tangent at the external point.
5. So the chord joining the points of contact is the segment that is perpendicularly bisected.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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