8. For all pairs of real numbers P and Q where P = 2Q + 9, Q = ?
1 answer:
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<u>Given:</u>
The circle has a diameter of 30 cm and a chord of 10 cm is drawn.
Radius of the circle = 15 cm
Half of the chord = 5 cm
We need to determine the distance of chord from the center of the circle.
<u>Distance of chord from the center of the circle:</u>
Let us use the Pythagorean theorem, to find the distance between the center and the chord.
Let d denote the distance between the center and the chord of the circle.
Thus, we get;
Taking square root on both sides, we get;
Thus, the distance between the center and the chord of the circle is 14.14 cm.
Hence, Option A is the correct answer.
1. Draw the points in the coordinate axes, as in the attached picture.
2. AB and CD are parallel, (both are parallel to the x-axis)
3. A is closer to the y axis than D and C is closer to the C closer than B
4. So combining 2 and 3, we conclude that ABCD is a trapezoid.
5. The remaining thing to check is whether the trapezoid is isosceles or not. For this we drop the heights to AB from points C and D,
and see that the distances from the feets of these heights to the points A and B are not equal.
Answer: Trapezoid
2. AB and CD are parallel, (both are parallel to the x-axis)
3. A is closer to the y axis than D and C is closer to the C closer than B
4. So combining 2 and 3, we conclude that ABCD is a trapezoid.
5. The remaining thing to check is whether the trapezoid is isosceles or not. For this we drop the heights to AB from points C and D,
and see that the distances from the feets of these heights to the points A and B are not equal.
Answer: Trapezoid