Q) Find the area of the shaded region in Figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD. (Use π = 22/7) Ans: We are given that an arc is drawn […]
triangles
Q) If a, b and c are the sides of a right angled triangle, where c is hypotenuse, then prove that the radius of the circle whichtouches the sides of the triangle is given by r = Ans: Let’s consider a right angled triangle ABC with sides a, b & c.Its ∠ A is right angle
If a, b and c are the sides of a right angled triangle, where c is hypotenuse, Read More »
Q) In figure, PQ is a tangent from an external point P to a circle with centre O and OP cuts the circle at T and QOR is adiameter. If ∠POR = 130° and S is a point on the circle, find ∠1 +∠2 Ans: In the given diagram, it is given that: ∠ POR
In figure, PQ is a tangent from an external point P to a circle with centre O Read More »
Q) In Fig. AD bisects ∠A, AB = 12 cm, AC = 20 cm and BD = 5 cm, determine CD. Ans: ∵ AD bisects ∠ A We know that, according to the angle bisector theorem, the angle bisector of a triangle divides the opposite side into two parts that are proportional to the other
In Fig. AD bisects ∠A, AB = 12 cm, AC = 20 cm and BD = 5 cm, determine CD. Read More »
Q) Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height of Vijay’s house if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground
Q) In the given figure, ∠ CEF = ∠ CFE. F is the midpoint of DC. Prove that . Ans: Step 1: From given conditions: ∵ ∠ CEF = ∠ CFE ∴ CE = CF (sides of opp. Angles) 2. ∵ F is midpoint of CD ∴ FD = CF ∴ CE = CF =
Q) PA and PB are tangents drawn to a circle of centre O from an external point P. Chord AB makes and angle of 30 with the radius at the point of contact. If length of the chord of 6 cm, find the length of the tangent PA and the length of the radius OA. Ans:
Q) Find the area of the unshaded region shown in the given figure. Ans: Let’s redraw the diagram: As we can see in the diagram, in the center area: diameter of semicircle (2R) = side of the inside square (S) or S = 2R ………………. (i) Also we see that Side of larger square = Gap
Find the area of the unshaded region shown in the given figure. Read More »
Q) With vertices A, B and C of Δ ABC as centres, arcs are drawn with radii 14 cm and the three portions of the triangle so obtained are removed. Find the total area removed from the triangle. Ans: We know that the area made by an arc of θ angle is given by = r2
Q) ABCD is a parallelogram. Point P divides AB in the ratio 2:3 and point Q divides DC in the ratio 4:1. Prove that OC is half of OA. Ans: Given that ABCD is a parallelogram. Therefore, AB ǁ CD and BC ǁ AD Since, Point P divides AB in the ratio 2:3 Therefore, if