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, AB^{2 }+ AC^{2 }= 290 cm^{2}, 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 a^{2 }+ b^{2 }= c^{2}, 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 2*a*.

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