# NCERT Class 10 Mathematics Higher Order Thinking Skills CBSE Board Sample Problems Part 2

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**Geometry**

31. In Fig. 1. ABC is an isosceles triangle with. P is a point on the side BC such that, and Prove that

32. InFig.2 and

Prove that

33. In a , D is the midpoint of side BC and . If Show that

34. In Fig. 3, XY and X’Y’ are two parallel tangents to a circle with Centre O and another tangent AB touching at C, intersecting XY at A and x y at B. Prove that

35. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of length 8 cm and 6 cm respectively. (See Fig.4). Find the sides AB and AC.

36. A round table cover has six equal designs as shown in figure on the side (shaded one). If the radius of the cover is 28 cm, find the cost of making the design at the rate of Rs. 0.35 per Use )

37. Two circles touch each other externally and the sum of their areas is . If the distance between the centres of two circles is 10 cm, find the radii of the two circles.

38. Find the area of the shaded region in the figure on the side where ABCD is a square of side 14 cm (Use).