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Prove that, if a line parallel to a side of a triangle intersects the other sides in two district points, then the line divides those sides in proportion.
Concept: Basic Proportionality Theorem (Thales Theorem)
ΔABP ~ ΔDEF and A(ΔABP) : A(ΔDEF) = 144:81, then AB : DE = ?
Concept: Similarity of Triangles
In ∆PQR, point S is the midpoint of side QR. If PQ = 11, PR = 17, PS = 13, find QR.
Concept: Right-angled Triangles and Pythagoras Property
Out of the following, which is the Pythagorean triplet?
Concept: Apollonius Theorem
Some question and their alternative answer are given.
In a right-angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?
Concept: Apollonius Theorem
Some question and their alternative answer are given. Select the correct alternative.
If a, b, and c are sides of a triangle and a2 + b2 = c2, name the type of triangle.
Concept: Right-angled Triangles and Pythagoras Property
In ΔMNP, ∠MNP = 90˚, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.
Concept: Right-angled Triangles and Pythagoras Property
In ΔPQR, seg PM is a median, PM = 9 and PQ2 + PR2 = 290. Find the length of QR.
Concept: Apollonius Theorem
Prove that “The lengths of the two tangent segments to a circle drawn from an external point are equal.”
Concept: Number of Tangents from a Point on a Circle
If two circles with radii 5 cm and 3 cm respectively touch internally, find the distance between their centres.
Concept: Theorem of Touching Circles
If two circles with radii 8 cm and 3 cm respectively touch externally, then find the distance between their centres.
Concept: Theorem of Touching Circles
Prove that “The opposite angles of a cyclic quadrilateral are supplementary”.
Concept: Theorem: Opposite angles of a cyclic quadrilateral are supplementary.
What is the distance between two parallel tangents of a circle having radius 4.5 cm ? Justify your answer.
Concept: Tangent to a Circle
Four alternative answers for the following question is given. Choose the correct alternative.
Two circles intersect each other such that each circle passes through the centre of the other. If the distance between their centres is 12, what is the radius of each circle?
Concept: Theorem of Touching Circles
∠ACB is inscribed in arc ACB of a circle with centre O. If ∠ACB = 65°, find m(arc ACB).
Concept: Inscribed Angle
Prove that the lengths of two tangent segments drawn to the circle from an external point are equal.
Concept: Number of Tangents from a Point on a Circle
`square`ABCD is cyclic. If ∠B = 110°, then find measure of ∠D.
Concept: Converse: If a Pair of Opposite Angles of a Quadrilateral is Supplementary, Then the Quadrilateral is Cyclic.
In the adjoining figure, circle with center D touches the sides of ∠ACB at A and B. If ∠ACB = 52°, find measure of ∠ADB.
Concept: Converse of Tangent Theorem
Chord AB and chord CD of a circle with centre 0 are congruent. If m(arc AB) = 120°, then find the m(arc CD).
Concept: Property of Sum of Measures of Arcs
If sinθ = cosθ, then what will be the measure of angle θ?
Concept: Theorem of Angle Between Tangent and Secant
