5. Prove that the perpendicular at the point of contact to the tangent

1.	5. Prove that the perpendicular at the point of contact to the tangent to a circle passesthrough the centre
Answer» Step-by-step EXPLANATION: Let O be the centre of the given circle. AB is the tangent drawn TOUCHING the circle at A. DRAW AC ⊥ AB at point A, such that point C lies on the given circle. ∠OAB = 90° (Radius of the circle is perpendicular to the tangent) Given ∠CAB = 90° ∴ ∠OAB = ∠CAB This is POSSIBLE only when centre O lies on the line AC. Hence, perpendicular at the point of CONTACT to the tangent to a circle passes through the centre of the circle.

5. Prove that the perpendicular at the point of contact to the tangent to a circle passesthrough the centre

Answer»

Step-by-step EXPLANATION:

Let O be the centre of the given circle. AB is the tangent drawn TOUCHING the circle at A. DRAW AC ⊥ AB at point A, such that point C lies on the given circle. ∠OAB = 90° (Radius of the circle is perpendicular to the tangent) Given ∠CAB = 90° ∴ ∠OAB = ∠CAB This is POSSIBLE only when centre O lies on the line AC. Hence, perpendicular at the point of CONTACT to the tangent to a circle passes through the centre of the circle.

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5. Prove that the perpendicular at the point of contact to the tangent to a circle passesthrough the centre​

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5. Prove that the perpendicular at the point of contact to the tangent to a circle passesthrough the centre