In the diagram below, O is circumscribed about quadrilateral ABCD. what is the value of x?
2 answers:
Answer:
(D)
Step-by-step explanation:
Given: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.
To find: the value of x.
Solution: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.
We know that the sum of opposite angles of the cyclic quadrilateral is 180°, therefore
Substituting the given values, we have
thus, the value of x is .
Hence, option D is correct.
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Answer:
G(3, 1), H(2, 3)
Step-by-step explanation:
When D is the midpoint of EG, it means ...
D = (E + G)/2
or
G = 2D -E = 2(3,4) -(3,7) = (2·3-3, 2·4-7) = (3, 1)
Likewise, H is ...
H = 2D -F = 2(3,4) -(4,5) = (2·3-4, 2·4-5) = (2, 3)
Answer:
The length of AC is 222 units.
Step-by-step explanation:
Given AC and AE are common external tangents of G and D.
BC= 123 , GB=20 and AG=101.
We have to find the measure of AC.
As, a straight line joined from the center i.e radius is perpendicular to tangent drawn. Therefore,
In ΔABG, by Pythagoras theorem
⇒
⇒
⇒ AB=99 units.
Hence, AC=AB+BC=99+123=222 units.
The length of AC is 222 units.