In the figure, the sides AC and BC are extended to the points 'Q' and 'P' respectively- If `angle A=angle P`
a) Write the equal angles of triangles ABC and 'PQC'.
b) Prové that `A C xx Q C=B C xx P C`

In the figure chord BC is extended to P. Tangent from P to the circle is PA. AQ is the bisector of angleBAC Write one pair of equal angles from that figure. .

In triangle 'ABC, angle B=90 degree . BD' is perpendicular to 'AC'. a) If 'angle A=x degree', find the measures of 'angle C' and 'angle ABD' b) Write the ratios of the sides opposite to the equal angles in triangle 'ABD' and triangle ABC. c) Prove that 'AB^2=AD x AC'.

In the figure, B P: P Q: Q C=1: 2: 1. Area of triangle APQ is 8 sq.cm. (a) Find the area of triangle A B P. b) Find the area of triangle ABC.

In the figure, O is the centre of both the circles. AB and AC touch the small circle at P and Q.A,B and C are points on the large circle. Prove that Ab=AC . .