A circle touches all four sides of a quadrilateral ABCD. If AB = 18 cm, BC = 21 cm and AD = 15 cm, then length CD is:
This questions was previously asked in
SSC CGL Tier II Paper 1 (02.03.2023)
Explanation:
To solve the problem and find the length of CD, let's look at the properties of a tangential quadrilateral:
- Property: In a quadrilateral where a circle can touch all four sides (also known as a tangential quadrilateral), the sum of the lengths of the opposite sides is equal, i.e., \(AB + CD = BC + AD\).
Now, let's apply this property:
- We know \(AB = 18\) cm, \(BC = 21\) cm, and \(AD = 15\) cm.
- Using the property, calculate \(CD\):
\[
AB + CD = BC + AD
\]
\[
18 + CD = 21 + 15
\]
\[
18 + CD = 36
\]
\[
CD = 36 - 18
\]
\[
CD = 18
\]
- Therefore, CD = 18 cm.
Option 4: 18 cm
.
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By: Parvesh Mehta