Question

The tangent at any point of a circle is perpendicular to the radius through the point of contact.​

Answer 1

Answer:

Theorem 4.1

Step-by-step explanation:

1. DATA : In the circle,

XY is the tangent. OP is the radius and P is point of contact.

2. TO PROVE : OP perpendicular to XY

3. CONSTRUCTION : Consider a point Q outside the circle and join OQ

4. PROOF : Here OQ>O

If we consider any other points on the line XY and If we join with the centre of the circle, then among all the lines drawn perpendicular is the shortest distance. Therefore OP is perpendicular to XY.

Hence Proved.

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