In the given fig., a triangle abc is drawn to circumscribe a circle of radius 3 cm, such that the segments bd and dc are respectively of lengths 6 cm and 9 cm. if the area of triangle abc is 54 cm2, then find the lengths of sides ab and ac.

In the given figure, two tangents rq and rp are drawn from an external point r to the circle with centre o. if angle prq = 120°, then prove that, or = pr + rq

X and y are points on the sides ab and ac respectively of a triangle abc such that 𝑨𝑿/𝑨𝑩, ay =2 cm and yc = 6cm. find whether xy is parallel to bc or not.

In the given fig., a circle is inscribed in a triangle abc, such that it touches the sides ab, bc and ca at points d, e and f respectively. if the lengths of sides ab, bc and ca are 12 cm, 8 cm and 10 cm respectively, find the lengths of ad, be and cf.

Find the ratio in which y-axis divides the line segment joining the points a(5, – 6) and b(– 1, – 4). also find the coordinates of the point of division.

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