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Circles

Question

In fig., a circle is inscribed in triangle ABC touches its sides AB, BC and ACat points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10cm, then find the length of AD, BE and CF.

Solution

$Given : AB = 12 cm, BC = 8 cm, and AC = 10 cm . Let, AD = AF = x cm, BD = BE = y cm, and CE = CF = z cm . (Tangents drwan from an external point to the circle are equal in length) \Rightarrow 2 (x + y + z) = AB + BC + AC = AD + DB + BE + EC + AF + FC = 30 cm . \Rightarrow x + y + z = 15 cm . AB = AD + DB = x + y = 12 cm ∴ z = CF = 15 - 12 = 3 cm AC = AF + FC = x + z = 10 cm ∴ y = BE = 15 - 10 = 5 cm ∴ x = AD = x + y + z - z - y = 15 - 3 - 5 = 7 cm .$

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Circles

In fig., a circle is inscribed in triangle ABC touches its sides AB, BC and ACat points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10cm, then find the length of AD, BE and CF.

Some More Questions From Circles Chapter

In the following figure, what are the angles of depression from the observing positions O₁ and O₂ of the object at A?

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For Daily Free Study Material Join wiredfaculty

Circles

In fig., a circle is inscribed in triangle ABC touches its sides AB, BC and ACat points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10cm, then find the length of AD, BE and CF.

Some More Questions From Circles Chapter

In the following figure, what are the angles of depression from the observing positions O1 and O2 of the object at A?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In the following figure, what are the angles of depression from the observing positions O₁ and O₂ of the object at A?