Discrete Math - Find X
1 answer:
Answer:
x = 70°
Step-by-step explanation:
Clockwise from top, call the three tangent points A, B, and C. Central angle AXC is the supplement of the marked external angle, so is 140°. Arc AB is bisected by the upper ray of angle x; and arc BC is bisected by the lower ray of angle x. That is to say x is half the measure of arc AC, so is 70°.
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Attached is the output of a geometry program. The angle at lower left is 40° as in the given figure. The central angle α (70°) remains the same as tangent point C is moved around, which is to say that the measure of the angle α does not depend on the dimensions of the triangle containing α. It just depends on the fact that the triangle is tangent to the circle.
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Answer:
The Proof for
△ABD ≅ △CBD is below
Step-by-step explanation:
Given:
AD = CD .........BD bisect AC
To Prove:
△ABD ≅ △CBD
Proof:
In ΔABD and ΔCBD
BD ≅ BD ....……….{Reflexive Property}
∠ADB ≅ ∠CDB …………..{Measure of each angle is 90°( )}
AD ≅ CD ....……….{ }
ΔABD ≅ ΔCBD .......….{By Side-Angle-Side Congruence test} ...Proved
