**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 AE^{2}+BD^{2}=AB^{2}+DE^{2} .

**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 AB^{2} = 2 AC^{2} + BC^{2} .

**Question 15.** In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. Prove that 9AD^{2}=7AB^{2}

**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°