Question

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

Answer 1

$\huge\mathfrak\red{HELLO}$

${Here}$${is}$${your}$ ${THEOREM:,}$

GIVEN: A tangent AB with point of contact P

TO PROVE THAT:AB⊥ OP

PROOF:Consider a point C on tangent AB other than P

Point C must lie outside the circle.

(°•°Tangent can have only one point of contact with the circle)

OC>OP (°•°C lies outside the circle)

OK is shortest distance between the point O & tangent AB.

AB⊥ OP

The shortest distance of a point from a line segment is the perpendicular distance of the point form the line segment.

Good luck for your exam!

#BE BRAINLY