Question

In a triangle ABC,D is a point on side BC such that angle ADC = Angle BAC. if CA = 12cm and CB =8Cm ,then CD is equal to??​

Answer 1

Answer:

Step-by-step explanation:

If d is mid point the it device cb into 1/2

: 1/2 of 8= 4 cm

Answer 2

Given : ∠ADC = ∠BAC

To find : CD

Solution :

in triangle BAC and ADC

$\angle ACB = \angle ACD \\\\\angle BAC = \angle ADC \\\\text{by AA similarity } \\\\\bigtriangleup BAC \sim \bigtriangleup ADC\\\\hence \\\\\frac{BA}{AD}=\frac{AC}{CD}=\frac{BC}{AC}$

(since the two triangle are similar their corresponding sides  are proportional )

hence ,

$\frac{AC}{CD}=\frac{BC}{AC}\\\\AC^2=BC\times CD$

Here , CA = 12 cm and CB = 8 cm

then

$CA^2=BC\times CD \\\\(12)^2 = 8\times CD\\\\144 = 8\times CD\\\\CD = \frac{144}{8}\\\\CD = 18$

hence ,The value of CD is 18 cm

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