Suppose a circle and a line intersect in a plane. what is the smallest number of points at which they can touch?

The smallest number of points at which they can touch is:

                                  1

Tangent of a circle--

The tangent to a circle is a straight line that touches the curve at just one point i.e. it " just crosses " the curve.

Hence, here it is given that a circle and a line intersect in the curve.

i.e. the line meets the circle at at least one point.

As the minimum number of intersection point is 1 (i.e. a tangent to the circle )

Hence, the answer is:

      1

-232

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°