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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, point T is in the interior of rectangle PQRS, Prove that, TS2 + TQ2 = TP2 + TR2 (As shown in the figure, draw seg AB || side SR and A-T-B)
Concept: Right-angled Triangles and Pythagoras Property
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
Out of the dates given below which date constitutes a Pythagorean triplet?
Concept: Pythagorean Triplet
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.
In ∆ABC, AB = \[6\sqrt{3}\] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.
Concept: Apollonius Theorem
Find the height of an equilateral triangle having side 2a.
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: Right-angled Triangles and Pythagoras Property
In ∆RST, ∠S = 90°, ∠T = 30°, RT = 12 cm, then find RS and ST.
Concept: Apollonius Theorem
In ∆ABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, Find AP.
Concept: Apollonius Theorem
∆ABC is an equilateral triangle. Point P is on base BC such that PC = `1/3`BC, if AB = 6 cm find AP.
Concept: Similarity in Right Angled Triangles
In a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)
Concept: Right-angled Triangles and Pythagoras Property
Find the length of the hypotenuse in a right angled triangle where the sum
of the squares of the sides making right angle is 169.
(A)15 (B) 13 (C) 5 (D) 12
Concept: Similarity in Right Angled Triangles
Prove that, in a right angled triangle, the square of the hypotenuse is
equal to the sum of the squares of remaining two sides.
Concept: Similarity in Right Angled Triangles
If hypotenuse of a right angled triangle is 5 cm, find the radius of
the circle passing through all vertices of the triangle.
Concept: Apollonius Theorem
In right angled triangle PQR,
if ∠ Q = 90°, PR = 5,
QR = 4 then find PQ and hence find tan R.
Concept: Similarity in Right Angled Triangles
Digonals of parallelogram WXYZ intersect at point O. If OY =5, find WY.
Concept: Right-angled Triangles and Pythagoras Property
In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.
Concept: Right-angled Triangles and Pythagoras Property
In right-angled triangle PQR, if ∠P = 60°, ∠R = 30° and PR = 12, then find the values of PQ and QR.
Concept: Property of 30°- 60°- 90° Triangle Theorem
Choose the correct alternative:
ΔABC and ΔDEF are equilateral triangles. If ar(ΔABC): ar(ΔDEF) = 1 : 2 and AB = 4, then what is the length of DE?
Concept: Similarity in Right Angled Triangles
