Deltoid Geometry: Calculate OC Given AO = 3cm and Triangle Ratio 1:3

Question

Shown below is the deltoid ABCD.

The ratio between triangle ABD and triangle BDC is 1:3.

Given in cm:

AO = 3

Calculate side OC.

00:00 Calculate OC

00:03 We'll use the formula for calculating the area of triangle ABD

00:13 We'll do the same for triangle BDC

00:20 We'll substitute these formulas in the triangles' ratio according to the given data

00:30 We'll simplify what we can

00:41 Size of AO according to the given data

00:46 We'll substitute the value of AO and solve for CO

00:51 And this is the solution to the question

To solve for $OC$ , follow these steps:

Step 1: Establish the area relationships. Given $\frac{\text{Area of } \triangle ABD}{\text{Area of } \triangle BDC} = \frac{1}{3}$ , these areas are proportional to segments $AO$ and $OC$ under height implications.
Step 2: Apply the area ratio property. Since areas are directly proportional to their corresponding triangle heights from a shared vertex, $\frac{AO}{OC} = \frac{1}{3}$ .
Step 3: Algebraically solve for $OC$ . Expressing proportions, $\frac{1}{3} \times OC = AO$ , gives $OC = 3 \times 3$ .
Step 4: Solve: $OC = 9 \, \text{cm}$ .

The accurate solution to the problem is $OC = 9 \, \text{cm}$ .

9 cm