In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason.
Concept: Property of three parallel lines and their transversals
In the given figure seg PS is the median of ∆PQR and PT ⊥ QR. Prove that,
\[{PR}^2 = {PS}^2 + QR \times ST + \left( \frac{QR}{2} \right)^2\]
Concept: Apollonius Theorem
In ∆ABC, point M is the midpoint of side BC.
If, AB2 + AC2 = 290 cm2, AM = 8 cm, find BC.
Concept: Apollonius Theorem
In the given figure, chord MN and chord RS intersect at point D.
(1) If RD = 15, DS = 4, MD = 8 find DN
(2) If RS = 18, MD = 9, DN = 8 find DS
Concept: Theorem of External Division of Chords
Some question and their alternative answer are given. Select the correct alternative.
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.
Out of the dates given below which date constitutes a Pythagorean triplet ?
Concept: Apollonius Theorem
Some question and their alternative answer are given. Select the correct alternative.
If a, b, c are sides of a triangle and a2 + b2 = c2, name the type of triangle.
Concept: Apollonius Theorem
Some question and their alternative answer are given. Select the correct alternative.
Find perimeter of a square if its diagonal is \[10\sqrt{2}\]
Concept: Apollonius Theorem
Some question and their alternative answer are given. Select the correct alternative.
Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.
Concept: Apollonius Theorem
Some question and their alternative answer are given. Select the correct alternative.
Height and base of a right angled triangle are 24 cm and 18 cm find the length of its hypotenuse
Concept: Apollonius Theorem
Some question and their alternative answer are given. Select the correct alternative.
In ∆ABC, AB = \[6\sqrt{3}\] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.
Concept: Apollonius Theorem
Solve the following example.
Find the height of an equilateral triangle having side 2a.
Concept: Apollonius Theorem
Do sides 7 cm, 24 cm, 25 cm form a right angled triangle ? Give reason
Concept: Apollonius Theorem
Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.
Concept: Apollonius Theorem
Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.
Concept: Apollonius Theorem
Find the centroid of the triangle whose vertice is given below.
(–7, 6), (2, –2), (8, 5)
Concept: Centroid Formula
Find the centroid of the triangle whose vertice is given below.
(3, –5), (4, 3), (11, –4)
Concept: Centroid Formula
Find the centroid of the triangle whose vertice is given below.
(4, 7), (8, 4), (7, 11)
Concept: Centroid Formula
In ∆ABC, G (–4, –7) is the centroid. If A (–14, –19) and B(3, 5) then find the co–ordinates of C.
Concept: Centroid Formula
