Question 1: Calculate the measure of the angle between the radius and tangent at the point of contact if the radius is 7 cm.

Answer: 90

Question 2: Construct a radius of length 5 cm and draw a tangent at its end point. Verify the angle formed.

Answer: Right angle (90 degrees)

Question 3: A circle has a radius of 6 cm. Draw a radius and a tangent at its end point. Label the right angle.

Answer: The angle between the radius and tangent is 90 degrees.

Question 1: In a circle, the radius is 8 cm. A tangent touches the circle at point T. If the radius OT is 8 cm, draw OT and the tangent at T, then mark the right angle.

Answer: 90 degrees

Question 2: Plot a circle with radius 4 cm. At a point on the circle, draw the radius and construct the tangent perpendicular to it. Confirm the right angle.

Answer: Right angle (90 degrees)

Question 3: A circle has a radius of 10 cm. Draw a radius from the center to a point on the circle. At the endpoint, draw the tangent perpendicular to the radius. Measure the angles.

Answer: 90 degrees

Question 1: A bike wheel is a circle with radius 35 cm. The mechanic draws a radius from the center to a point on the rim and then draws a tangent at that point. Explain why the tangent is perpendicular to the radius.

Answer: Because the tangent to a circle is perpendicular to the radius at the point of contact.

Question 2: A circular fountain has a radius of 10 meters. A worker draws a radius and then constructs a tangent to the circle at a point on the rim. Why must the tangent form a 90-degree angle with the radius?

Answer: Because the property states that the tangent is perpendicular to the radius at the point of contact.

Question 1: Construct a circle with radius 6 cm. From a point outside the circle, draw two tangents touching the circle. Show that the angles between the radii and tangents are both 90 degrees and that the tangents are equal in length.

Answer: Angles are 90 degrees; tangent lengths are equal.

Question 2: Given a circle with radius 9 cm, a point P outside the circle is 15 cm from the center. Draw the two tangents from P to the circle. Calculate the length of each tangent from P to the point of contact.

Answer: Using Pythagoras: sqrt(15^2 - 9^2) = sqrt(225 - 81) = sqrt(144) = 12 cm

Question 1: In a circle with radius 5 cm, draw a radius and a tangent at its end point. Measure and verify the right angle.

Answer: 90 degrees

Question 2: A circle has radius 12 cm. From a point outside the circle, draw two tangents. Show that the angles between the line connecting the point and the circle's center are equal.

Answer: The tangents are equal in length, and the angles between the lines from the outside point are equal.

Question 1: A student draws a radius and a tangent but marks the angle at the tangent point as 60°. Identify and explain the mistake.

Answer: The mistake is assuming the angle is 60°, but the angle between radius and tangent at contact must be 90°.

Question 2: A student draws a tangent that is not perpendicular to the radius at contact. What correction should be made?

Answer: The student should draw the tangent so that it forms a right angle (90°) with the radius at the point of contact.