Give me a stock clerk with a goal, and I will give you a man who will make history. Give me a man without a goal, and I will give you a stock clerk. – **J.C. Penny**

# Lecture - 11 Chapter 6 Triangles

**NCERT Exercise 6.5 (Part 1)**

**Question 8.** In Fig. 6.54, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that

(i) OA^{2}+OB^{2}+OC^{2}-OD^{2}-OE^{2}-OF^{2}=AF^{2}+BD^{2}+CE^{2}

(ii) AF^{2}+BD^{2}+CE^{2}=AE^{2}+CD^{2}+BF^{2}

**Question 9.** A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.

**Question 10.** A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

**Question 11.** An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after \( 1 \frac{1}{2} \) hours?

NCERT Exercise 6.5 (Part 2)

Question 12. Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.

Question 13. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2+BD2=AB2+DE2 .

Question 14. The perpendicular from A on side BC of a ∆ ABC intersects BC at D such that DB = 3 CD (see Fig. 6.55). Prove that 2 AB2 = 2 AC2 + BC2 .

Question 15. In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. Prove that 9AD2=7AB2

Question 16. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Question 17. Tick the correct answer and justify : In ∆ ABC, AB = 6 3 cm, AC = 12 cm and BC = 6 cm. The angle B is :

(A) 120°

(B) 60°

(C) 90°

(D) 45°