In the given figure (not drawn to scale), BC is parallel to EF, CD is parallel to FG, AE : EB = 2 : 3, ∠BAD = 70°, ∠ACB = 105°, ∠ADC = 40° and AC is bisector of ∠BAD.

(a) Prove Δ AEF ~ Δ AGF

(b) Find :

(i) AG : AD

(ii) area of Δ ACB: area Δ ACD

(iii) area of quadrilateral ABCD: area of Δ ACB.

In the given figure, angle ABC = 70° and angle ACB = 50°. Given, O is the centre of the circle and PT is the tangent to the circle. Then calculate the following angles

(a) ∠CBT

(b) ∠BAT

(c) ∠PBT

(d) ∠APT

(a) Construct a triangle ABC such that BC = 8 cm, AC = 10 cm and ∠ABC = 90°.

(b) Construct an incircle to this triangle. Mark the centre as I.

(c) Measure and write the length of the in-radius.

(d) Measure and write the length of the tangents from vertex C to the incircle.

(e) Mark points P, Q and R where the incircle touches the sides AB, BC, and AC of the triangle respectively. Write the relationship between ∠RIQ and ∠QCR.

(Use a ruler and a compass for this question.)

A bag contains 13 red cards, 13 black cards and 13 green cards. Each set of cards are numbered 1 to 13. From these cards, a card is drawn at random. What is the probability that the card drawn is a:

(a) green card?

(b) a card with an even number?

(c) a red or black card with a number which is a multiple of three?