Q1. If a circle has a radius of 5 cm, what is the length of a chord that is 4 cm away from the center of the circle?
Solution:
Using the Pythagorean theorem, the length of the chord can be calculated as 2 * sqrt(5^2 - 4^2) = 6 cm.
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Q2. If two angles are supplementary and one angle measures 40 degrees, what is the measure of the other angle?
Solution:
Supplementary angles add up to 180 degrees, so the other angle measures 180 - 40 = 140 degrees.
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Q3. What is the measure of an angle formed by a tangent and a chord through the point of contact?
Solution:
The angle formed by a tangent and a chord through the point of contact is equal to the angle subtended by the chord at the circumference.
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Q4. In triangle ABC, if angle A is 50 degrees and angle B is 60 degrees, what is the measure of angle C?
Solution:
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (50 + 60) = 70 degrees.
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Q5. If two angles are corresponding angles formed by a transversal intersecting two parallel lines, what can be said about their measures?
Solution:
Corresponding angles are equal when a transversal intersects two parallel lines.
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Q6. If a circle has a radius of 5 cm, what is the length of a chord that is 4 cm away from the center?
Solution:
Using the Pythagorean theorem, the length of the chord is 2√(5^2 - 4^2) = 2√9 = 6 cm.
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Q7. What is the sum of the interior angles of a triangle formed by two intersecting chords in a circle?
Solution:
The sum of the interior angles of any triangle is always 180 degrees.
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Q8. If two angles are alternate exterior angles when two parallel lines are cut by a transversal, what can be concluded?
Solution:
Alternate exterior angles are equal when two parallel lines are cut by a transversal.
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Q9. If a circle has a radius of 5 cm, what is the length of a chord that is 6 cm away from the center?
Solution:
Using the Pythagorean theorem, the length of the chord can be calculated as 2 * sqrt(5^2 - 6^2) = 2 * sqrt(25 - 36) = 2 * sqrt(-11), which is not possible. The chord cannot exist.
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Q10. What is the measure of each angle formed by two parallel lines cut by a transversal if one angle measures 75 degrees?
Solution:
The corresponding angle will measure 75 degrees, and the alternate interior angle will measure 105 degrees.
