A tangent to a circle is drawn from a point outside the circle. If the radius of
Practice Questions
Q1
A tangent to a circle is drawn from a point outside the circle. If the radius of the circle is 3 cm and the distance from the center to the point is 5 cm, what is the length of the tangent?
4 cm
6 cm
5 cm
3 cm
Questions & Step-by-Step Solutions
A tangent to a circle is drawn from a point outside the circle. If the radius of the circle is 3 cm and the distance from the center to the point is 5 cm, what is the length of the tangent?
Step 1: Identify the radius of the circle (r) and the distance from the center of the circle to the point outside the circle (d). Here, r = 3 cm and d = 5 cm.
Step 2: Use the formula for the length of the tangent (L) from a point outside the circle: L = √(d² - r²).
Step 3: Calculate d² (the square of the distance from the center to the point): d² = 5² = 25.
Step 4: Calculate r² (the square of the radius): r² = 3² = 9.
Step 5: Subtract r² from d²: 25 - 9 = 16.
Step 6: Take the square root of the result: √16 = 4.
Step 7: Conclude that the length of the tangent is 4 cm.
Tangent to a Circle – The length of a tangent from a point outside a circle can be calculated using the formula: Length of tangent = √(d² - r²), where d is the distance from the center of the circle to the external point and r is the radius of the circle.
Pythagorean Theorem – The relationship between the radius, the distance from the center to the external point, and the tangent forms a right triangle, which can be analyzed using the Pythagorean theorem.
