321.Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.
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322.Points P, Q, R and S in that order are dividing a line segment joining A(2, 6) and B(7, 4) in five equal parts. Find the co-ordinates of P and R.
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323.BL and CM are median of a triangle ABC right angled at A. Prove that 4(BL2 + CM2) = 5BC2.
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324.
In the given Fig, ABC is a right triangle, right angled at B. AD and CE are two medians drawn from A and C respectively. If AC = 5 cm and find the length of CE.
325.In an isosceles triangle ABC, with AB = AC, BD is perpendicular from B to the side AC. Prove that BD2 - CD2 = 2CD.AD.
An isosceles triangle ABC, with AB = AC. BD is perpendicular from B to the side AC. To Prove: BD2 - CD2 = 2CD.AD
Proof : In right triangle ABD, AB2 = AD2 + BD2 [Using Pythagoras theorem] But AB = AC ⇒ AC2 = AD2 + BD2 ⇒ (AD + DC)2 = AD2 + BD2 ⇒ AD2 + DC2 + 2AD.DC = AD2 + BD2 ⇒ 2AD.DC = BD2 - DC2 ⇒ BD2 - DC2 = 2AD.CD.
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Long Answer Type
326.ABC is a triangle in which AB = AC and D is any point in BC. Prove that AB2 - AD2 = BD.CD.
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327.In a right triangle ABC, right angled at C.P. and Q are the points on the sides CA and CB respectively, which divdes these sides in the ratio 2:1. Prove that (i) 9AQ2 9AC2 + 4BC2 (ii) 9BP2 9BC2 + 4AC2 (iii) 9(AQ2 + BP2) = 13AB2.
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328.In the given figure ABC is a triangle right angled at B. P and Q trisect BC. Prove that: 8AP2 = 3AC2 + 5AQ2
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329.
In the given Fig., ∠ACB = 90° and CD ⊥ AB. Prove that
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330.P and Q are points on sides CA and CB respectively of ∆ABC, right angled at C. Prove that AQ2 + BP2 = AB2 + PQ2.
Long Answer Type
find the length of CE.
Short Answer Type
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