In Fig. 10.97, the sides `A B ,\ B C` and `C A` of triangle `A B C` , touch a circle at `P ,\ Q` and `R` respectively. If `P A=4c m` , `B P=3c m` and `A C=11 c m` , then length of `B C` is (FIGURE) (a) 11cm (b) 10cm (c) 14cm (d) 15cm

In Fig. 10.20, the sides A B ,\ B C and C A of triangle A B C touch a circle with centre O and radius r at P ,\ Q and R respectively. (FIGURE) Prove that: 1) AB + CQ = AC + BQ

In Figure, the perimeter of A B C is (a) 30cm (b) 60cm (c) 45cm (d) 15cm

In Fig. 10.94, if A B=8c m and P E=3c m , then A E= (FIGURE) (a) 11cm (b) 7cm (c) 5cm (d) 3cm

If A B C D E F such that D E=3c m , E F=2c m , D F=2. 5 c m , B C=4c m , then perimeter of A B C is (a) 18cm (b) 20cm (c) 12cm (d) 15cm

In the adjacent figure, if A B=12 c m ,\ \ B C=8c m and A C=10 c m , then A D= (a) 5cm (b) 4cm (c) 6cm (d) 7cm

In Figure, a quadrilateral A B C D is drawn to circumscribe a circle such that its sides A B ,\ B C ,\ C D and A D touch the circle at P ,\ Q ,\ R and S respectively. If A B=x\ c m , B C=7c m , C R=3c m and A S=5c m , then x= (a) 10 (b) 9 (c) 8 (d) 7

In an isosceles triangle A B C , if A B=A C=25 c m and B C=14 c m , then the measure of altitude from A on B C is (a) 20cm (b) 22cm (c) 18cm (d) 24cm

In A B C , P and Q are points on sides A B and A C respectively such that P Q ||B C . If A P=3c m , P B=5c m and A C=8c m , find A Q .

In A B C , P and Q are points on sides A B and A C respectively such that P Q||B C . If A P=4c m ,\ \ P B=6c m and P Q=3c m , determine B C .

In Figure, A B C D is a parallelogram. If A B=12\ c m ,\ \ A E=7. 5\ c m ,\ C F=15\ c m , then A D= (a) 3 cm (b) 6 cm (c) 8 cm (d) 10.5 cm