Q) If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA. Ans: Let’s first draw a diagram for the given question: Let ABCDEF be the Heaxagon which is circumscribed on a circle. This circle has Center O and radius R. Now let P, Q, R, […]
If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA. Read More »
Q) A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners A, B and C respectively, of a grassy triangular field ABC with sides of lengths 35 m, 40 m and 50 m. Find the total area of grass field that can be grazed by them.
A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners Read More »
Q) A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and AB = 24 cm, find the radius of the circle Ans: Let’s first draw a diagram for the given question: By Pythagorus theorem, AC = = = = 25 cm Method 1: OP = OQ (radius of
Q) An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find:(i) the length of the arc(ii) the area of the minor segment of the circle made by the corresponding chord radius r of in-circle. Ans: Let’s draw the diagram for better understanding: (i) length of the arc: We
Q) Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu. During the festival of Onam , your school is planning to conduct a Pookalam competition. Your friend who is a partner in competition, suggests two designs given below. Observe
Pookalam is the flower bed or flower pattern designed during Onam in Kerala. Read More »
Q) In figure 1, a right triangle ABC in which ∠B = 90 is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC. Ans: Here is the step by step solution method: Step 1: We can see that, Q
Q) PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are drawn such that PQ = QR = RS. Semicircles are drawn on PQ and QS as diameters as shown in figure. Find the perimeter and area of the shaded region. Ans: Given that the
Q) Find upto three places of decimal the radius of the circle whose area is the sum of the areas of two triangles whose sides are 35, 53, 66 and 33, 56, 65 measured in centimeters (Use π = ) Ans: Let’s start with calculating area of triangles: In 1st triangle: sides a = 35 cm,
Q) In the given figure, ABC is a triangle in which ∠B = 900, BC = 48 cm and AB = 14 cm. A circle is inscribed in the triangle, whose centre is O. Find radius r of in-circle. Ans: By Pythagorus theorem, AC = = = = 50 cm Method 1: OP = OQ (radius
In the given figure, ABC is a triangle in which ∠B = 90, BC = 48 cm and AB = 14 cm. Read More »
Q) A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the figure. Prove that AB + CD = AD + BC Ans: By tangents property, we know that the tangents drawn on a circle from an external point are always equal, ∴ from Point A: AP = AS ………….. (i) from Point B: