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Vinil7 [7]
3 years ago
5

Two tangents drawn to a circle from a point outside it, are equal in length.prove it.​

Mathematics
1 answer:
stiks02 [169]3 years ago
7 0
Given: A circle with centre O; PA and PB are two tangents to the circle drawn from an external point P.
To prove: PA = PB
Construction: Join OA, OB, and OP.
It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.
OA⊥PA
OB⊥PB
In △OPA and △OPB
∠OPA=∠OPB (Using (1))
OA=OB (Radii of the same circle)
OP=OP (Common side)
Therefor △OPA≅△OPB (RHS congruency criterion)
PA=PB
(Corresponding parts of congruent triangles are equal)
Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.
The length of tangents drawn from any external point are equal.
So statement is correct

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4 0
3 years ago
A restaurant served Six slices of pie during lunch and lunch and 4 during dinner today how many slices of pie were served today
rewona [7]

Answer:

10 (?)

Step-by-step explanation:

6 during lunch + 4 during dinner would be 10. Not sure why you said lunch twice.

7 0
3 years ago
During a 20% off sale, the sale price of a bluetooth radio was $33.96. What was the regular price?
SVETLANKA909090 [29]

20% of the regular price was off.

So 80% of the regular price stayed on.

$33.96 was that 80% of the regular price.

(0.8) · (regular price)  =  $33.96

Divide both sides by (0.8).

Regular price =  ($33.96) / (0.8)

<em>Regular price = $42.45</em>

5 0
2 years ago
Rania solves the equation below by first squaring both sides of the equation.
Anuta_ua [19.1K]

Answer:

The extraneous solution is 4.

Step-by-step explanation:

First, let us calculate the value of 'x' without squaring both side of the expression. This is illustrated below:

-5 = 3x - 7

Collect like terms

-5 + 7 = 3x

2 = 3x

Divide both side by 3

x = 2/3.

Now, let us calculate the value of 'x' by squaring both side of the expression. This is illustrated below:

(-5)^2 = (3x - 7)^2

25 = (3x - 7)(3x - 7)

25 = 9x^2 - 21x - 21x + 49

9x^2 - 42x + 49 - 25 = 0

9x^2 - 42x + 24 = 0

Solving by factorisation:

Multiply the first term i.e 9x^2 and 3rd term i.e 24 together. The result is 216x^2.

Next, we shall obtain two factors of 216x^2 such that when we add them together, it will give the 2nd term i.e -42x in the equation. These factors are: -6x and -36x

Now we can write the above equation as:

9x^2 - 42x + 24 = 0

9x^2 - 6x - 36x + 24 = 0

3x(3x - 2) - 12(3x - 2) = 0

(3x - 12)(3x - 2) = 0

3x - 12 = 0 or 3x - 2 = 0

3x = 12 or 3x = 2

x = 12/3 or x = 2/3

x = 4 or 2/3.

We can see that when we solve the question without squaring both side, the value of x is 2/3. But when we solve by squaring both side, the value of x are 4 and 2/3.

Therefore, the extraneous solution to the question is 4.

6 0
3 years ago
A map of your town has a scale of 1 inch to 0.25 mile. There are two roads that are 5 inches apart on the map. Use this informat
egoroff_w [7]

Answer: <u>The 2 roads are 1.25 miles apart.</u>

Step-by-step explanation:

If 1 inch equals .25 miles, then you need to multiply .25 by 5.

Use proportions. Make sure the miles are on the same "side" of the fraction. Side meaning the top or the bottom

\frac{1}{.25} =\frac{5}{x}

1 times X equals 1x

.25 times 5 equals 1.25

1.25 divided by 1 equals 1.25.

6 0
3 years ago
Read 2 more answers
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