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NCSSM PLACEMENT EXAM 2025/2026 LATEST QUESTIONS &
ANSWERS 100% ACCURATE SOLUTIONS FOR GUARANTEED
SUCCESS | EXPERT-VERIFIED, GRADED A+
Area of a circle
pi times radius squared.
Central angle
is equal to its intercepted arc.
Inscribed angle
is equal to ½ its intercepted arc.
Angle formed by 2 chords intersecting in a circle
is equal to the sum of the arcs divided by 2.
Angle formed by 2 secants
is equal to the major arc minus the minor arc divided by 2.
Angle formed by a secant and a tangent
is equal to the major arc minus the minor arc divided by 2.
Tangent
intersects a circle in only 1 place.
Secant
intersects a circle in 2 places.
Intersection of a tangent and a radius
form right angles when they intersect.
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Equation of a circle
x minus h squared plus y minus k squared equals radius squared.
Circumference of a circle
2 times pi times radius or pi times diameter.
Angle formed by two tangents
is equal to the major arc minus the minor arc divided by 2.
Lengths of 2 intersecting chords
part of the first chord times the other part of the first chord equals a part of the
second chord times the other part of the second chord.
Lengths of an intersecting diameter and chord that meet at right angles
(perpendicular)
if a diameter meets a chord at a right angle (perpendicular), the diameter divides
the chord into 2 equal parts.
Lengths of 2 intersecting secants
the whole length of the first secant times the outside length of the first secant
equals the whole length of the second secant times the outside length of the
second secant.
Lengths of an instersecting secant and tangent
the whole length of the first secant times the outside length of the first secant
equals the length of the tangent squared.
Lengths of intersecting tangents
Tangents to a circle sharing a common vertex are equal.
Angles
acute angles are less than 90 degrees. Right angles are 90 degrees. obtuse angles
are between 90 and 180 degrees. Straight angles are 180 degrees and reflex
angles are greater than 180 degrees.
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Adjacent angles
share a common vertex, a common side, but not common interior points.
Complementary angles
2 angles when added together that equal 90 degrees.
They do not have to be adjacent angles.
Supplementary angles
2 angles when added together that equal 180 degrees.They do not have to be
adjacent angles.
Vertical angles
vertical angles are congruent.
Alternate interior angles
alternate interior angles are congruent.
Corresponding angles
corresponding angles are congruent.
Sum of the angles in a triangle
the 3 angles of a triangle add up to 180 degrees.
Triangles classified by sides
scalene triangles have no equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.
Triangles classified by angles
acute triangles have 3 acute angles.
right triangles have a 90 degree and 2 acute angles.
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obtuse triangles have an obtuse and 2 acute angles.
Exterior angle of a triangle
the exterior angle of a triangle equals the sum of the 2 opposite interior angles.
Isosceles triangles
sides opposite congruent angles are congruent.
angles opposite congruent sides are congruent.
Triangle inequality theorem
the sum of 2 sides of a triangle must be greater than the 3rd side.
Mid segment of a triangle
a mid segment connects the midpoint of 2 sides of a triangle and is equal to ½ the
side not containing the 2 midpoints.
Median
bisects the opposite side into 2 congruent line segments.
they meet in a triangle at a point called the centroid.
median segments are in a ratio of 2 to 1.
Angle bisector
bisects an angle into 2 congruent angles.
they meet in a triangle at a point called the incenter.
Altitude
makes a right angle with the opposite side.
they meet in a triangle at a point called the orthocenter.
Perpendicular bisector
bisects and makes a right angle with a side of a triangle.They meet in a triangle at
a point called the circumcenter.
NCSSM PLACEMENT EXAM 2025/2026 LATEST QUESTIONS &
ANSWERS 100% ACCURATE SOLUTIONS FOR GUARANTEED
SUCCESS | EXPERT-VERIFIED, GRADED A+
Area of a circle
pi times radius squared.
Central angle
is equal to its intercepted arc.
Inscribed angle
is equal to ½ its intercepted arc.
Angle formed by 2 chords intersecting in a circle
is equal to the sum of the arcs divided by 2.
Angle formed by 2 secants
is equal to the major arc minus the minor arc divided by 2.
Angle formed by a secant and a tangent
is equal to the major arc minus the minor arc divided by 2.
Tangent
intersects a circle in only 1 place.
Secant
intersects a circle in 2 places.
Intersection of a tangent and a radius
form right angles when they intersect.
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Equation of a circle
x minus h squared plus y minus k squared equals radius squared.
Circumference of a circle
2 times pi times radius or pi times diameter.
Angle formed by two tangents
is equal to the major arc minus the minor arc divided by 2.
Lengths of 2 intersecting chords
part of the first chord times the other part of the first chord equals a part of the
second chord times the other part of the second chord.
Lengths of an intersecting diameter and chord that meet at right angles
(perpendicular)
if a diameter meets a chord at a right angle (perpendicular), the diameter divides
the chord into 2 equal parts.
Lengths of 2 intersecting secants
the whole length of the first secant times the outside length of the first secant
equals the whole length of the second secant times the outside length of the
second secant.
Lengths of an instersecting secant and tangent
the whole length of the first secant times the outside length of the first secant
equals the length of the tangent squared.
Lengths of intersecting tangents
Tangents to a circle sharing a common vertex are equal.
Angles
acute angles are less than 90 degrees. Right angles are 90 degrees. obtuse angles
are between 90 and 180 degrees. Straight angles are 180 degrees and reflex
angles are greater than 180 degrees.
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Adjacent angles
share a common vertex, a common side, but not common interior points.
Complementary angles
2 angles when added together that equal 90 degrees.
They do not have to be adjacent angles.
Supplementary angles
2 angles when added together that equal 180 degrees.They do not have to be
adjacent angles.
Vertical angles
vertical angles are congruent.
Alternate interior angles
alternate interior angles are congruent.
Corresponding angles
corresponding angles are congruent.
Sum of the angles in a triangle
the 3 angles of a triangle add up to 180 degrees.
Triangles classified by sides
scalene triangles have no equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.
Triangles classified by angles
acute triangles have 3 acute angles.
right triangles have a 90 degree and 2 acute angles.
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obtuse triangles have an obtuse and 2 acute angles.
Exterior angle of a triangle
the exterior angle of a triangle equals the sum of the 2 opposite interior angles.
Isosceles triangles
sides opposite congruent angles are congruent.
angles opposite congruent sides are congruent.
Triangle inequality theorem
the sum of 2 sides of a triangle must be greater than the 3rd side.
Mid segment of a triangle
a mid segment connects the midpoint of 2 sides of a triangle and is equal to ½ the
side not containing the 2 midpoints.
Median
bisects the opposite side into 2 congruent line segments.
they meet in a triangle at a point called the centroid.
median segments are in a ratio of 2 to 1.
Angle bisector
bisects an angle into 2 congruent angles.
they meet in a triangle at a point called the incenter.
Altitude
makes a right angle with the opposite side.
they meet in a triangle at a point called the orthocenter.
Perpendicular bisector
bisects and makes a right angle with a side of a triangle.They meet in a triangle at
a point called the circumcenter.
