Question
Download Solution PDFIn a ΔABC. D is point on BC. AB is produce to E and AC is produce to F. A circle is passes through DEF, where AB = 10 cm, AC = 8.6 cm and BC = 6.4, then BE = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
From the same external point, the tangent segments to a circle
are equal.
Calculation:
Given, AB = 10 cm, AC = 8.6 cm and BC = 6.4 cm
Let BE = x cm and CF = y cm
As we know,
BE = BD [tangents]
DC = CF [tangents]
AE = AF [tangents]
AB + BE = AC + CF
⇒ 10 + x = 8.6 + y
⇒ x – y = 8.6 – 10
⇒ x – y = - 1.4 ----(1)
BD + DC = 6.4
⇒ x + y = 6.4 ----(2)
From equation (1) and equation (2)
⇒ x = 2.5
∴ BE = 2.5 cm
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