Solved Problems on Tangent Secant Theorem
Example 1: Find the value of x.
Solution:
Total length of the secant = 6 + 10 = 16
By the tangent secant theorem
AB2 = AC Γ AD
β x2 = 6 Γ 16
β x2 = 96
β x = 4β6
Example 2: Find the total length of the secant.
Solution:
By the tangent secant theorem
AB2 = AC Γ AD
β 102 = 6 Γ (x + 2)
β (x + 2) = 100 / 6
β (x + 2) = 16.66
Total length of the secant CD = x + 2 = 16.66 = 14.66
Example 3: Find the length of the tangent.
Solution:
By the tangent secant theorem
AB2 = AC Γ AD
β z2 = 8 Γ 15
β z2 = 120
β z = 2β30
Example 4: Find the value of x.
Solution:
By the tangent secant theorem
AB2 = AC Γ AD
β 122 = x Γ (x + 5)
β 144 = x2 + 5x
β x2 + 5x β 144= 0
β x = 9.75 or x = -14.75 (length cannot be negative)
Thus, x = 9.75
Example 5: Find the value of x and y.
Solution:
By the tangent secant theorem
AB2 = AC Γ AD
β 92 = x Γ 12
β x = 81 / 12
β x = 6.75
From the above figure
x + y = 12
β y = 12 β x
β y = 12 β 6.75
β y = 5.25
Tangent Secant Theorem
Tangent Secant Theorem is the fundamental theorem in geometry. Tangent and secant are the important parts of the circle. The tangent secant theorem is used in various fields of mathematics, construction, and many more. Tangents and secants are the lines that intersect the circle at some points.
In this article, we will learn about the Tangent Secant theorem in detail along with its statement and proof. It also covers the applications and limitations of the tangent secant theorem and some solved examples of the Tangent Secant Theorem. Letβs start our learning on the topic Tangent Secant theorem.
Table of Content
- What is Tangent and Secant?
- What is Tangent Secant Theorem?
- Proof of Tangent Secant Theorem
- Limitation and Applications of Tangent Secant Theorem
- Solved Problems
- FAQs
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