a circle is inscribed in a triangle ABC having sides bc=8cm Ab=10cm and Ac=12cm find the length BL, CM, and AN
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Answers
Step-by-step explanation:
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Concept:
For this question we must understand:
Tangents from a given given external points are the same.
Given:
A circle is inscribed in a triangle ABC
BC=8 cm, AB=10 cm, AC=12 cm
To find:
The values of BL, CM, AN.
Solution:
Since, now we know Tangents from a given given external points are the same.
AN=AM --------(1)
BM=BL --------(2)
CN=CL --------(3)
Let,
CN=CL=x
Therefore, from equation (1) and (3)
AN+CN=12 ⇒ AN=12-CN ⇒ AN=12-x ⇒ AN=AM=12-x ----(4)
CL+LB=8 ⇒ LB=8-CN ⇒ LB=8-x ⇒ LB=BM=8-x -------(5)
Now,
AB=AM+MB
⇒ AB= (12-x)+(8-x) [ From equation (4) and (5) ]
Since AB=10
⇒ 10= 20-2x
⇒ 2x=20-10
⇒ 2x=10
⇒ x=5 cm
Therefore
CM=x=5 cm
BL= 8-x = 8-5= 3 cm
AN = 12-x= 12-5 = 7 cm
Therefore, value of CM, BL, AN is 5 cm, 3 cm and 7 cm respectively.
