Question

In a triangle, ABC, D, E, F are points on BC, AC, and AB respectively. AD, BE and CF are concurrent civilians. BD/DC = CF/FA = (Means angle ADB= Angle AFC) = 35 deg = 65 deg Find

Answer 1

Answer:

Answer: A triangle which has all its sides unequal, is called a scalene triangle. A triangle which has two of its sides equal and one unequal is called an isosceles triangle. A triangle which has all its sides equal is known as an equilateral triangle.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h. This formula is applicable to all types of triangles, whether it is a scalene triangle, an isosceles triangle or an equilateral triangle.

Step-by-step explanation:

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Answer 2

Solution :

In order to prove that the points B,C,E and D are concyclic, it is sufficient to show that ∠ABC + ∠CED = 180° and ∠ACB + ∠BDE = 180°

In △ABC, we have

AB=AC and AD=AE

➡AB−AD=AC−AE

➡ DB=EC

Thus, we have

AD = AE and DB = EC

➡ AD/ DB = AE /EC

➡DE ∣∣ BC [By the converse of Thale's Theorem]

➡∠ABC=∠ADE [Corresponding angles]

➡∠ABC+∠BED=∠ADE+∠BDE [Adding ∠BDE both sides]

➡ ∠ABC+∠BDE=180°

➡∠ACB+∠BDE = 180°

[∵AB=AC∴∠ABC=∠ACB]

Again, DE ∣∣ BC

➡ ∠ACB=∠AED

➡ ∠ACB+∠CED=∠AED+∠CED [Adding ∠CE on both sides]

➡ ∠ACB+∠CED=180°

➡∠ABC+∠CED=180°

[∵∠ABC=∠ACB]

Thus :

BDEC is a cyclic quadrilateral. Hence, B,C,E and D are concyclic points.