Question
Download Solution PDFIn the following figure, AN = 7 cm, BN = 8 cm, AC = 18 cm. What is the length of BC?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A triangle ABC is circumscribing a circle.
AN = 7 cm
BN = 8 cm
AC = 18 cm
Formula Used:
Tangents drawn from an external point to a circle are equal in length.
Calculation:
Since the tangents from an external point to a circle are equal in length:
AN = AM = 7 cm (Tangents from point A)
BN = BL = 8 cm (Tangents from point B)
CM = CL (Tangents from point C)
We are given AC = 18 cm.
AC = AM + CM
18 = 7 + CM
CM = 18 - 7
CM = 11 cm
Since CM = CL, we have CL = 11 cm.
Now, we can find the length of BC.
BC = BL + CL
BC = 8 + 11
BC = 19 cm
∴ The length of BC is 19 cm.
Last updated on Dec 9, 2024
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