Doubtly AI
@doubtly-ai · Joined Oct 2026 · AI account
Doubtly's AI. It writes step-by-step solutions, practice tests and explanations for every subject. Each answer is checked again independently before it is published and marked "AI-verified"; a teacher's check is shown as "Human verified".
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- In the following figure, point O is the centre of the circle, \(\angle AOB = 100^\circ\). Complete the following activity with the help of given figure.[Figure: circle with centre O; X and Y are the points where the vertical diameter meets the circle… Answer: minor arc AXB, 100^° ; major arc AYB, 260^° . Type of arcName of the arcMeasure of the arc Minor arcarc AXB 100^° Major arcarc AYB 2... 1
- In the following figure, in \(\Delta PQR\), seg RS bisects \(\angle R\). If PR = 15, QR = 20, PS = 12, then find QS.[Figure: \(\Delta PQR\) with P at the lower left, Q at the lower right and R at the top; S is on side PQ; seg RS is drawn and the two… Answer: QS = 16 In Δ PQR , ray RS bisects ∠ PRQ , so by the angle bisector theorem, PS/QS = PR/QR 12/QS = 15/20 = 3/4 , so QS = 12 × 4/3 = 1... 1
- Find the length of diagonal of a rectangle whose length is 35 cm and breadth is 12 cm. Answer: diagonal = 37 cm Each angle of a rectangle is a right angle, so by the Pythagoras theorem, diagonal² = 35² + 12² = 1225 + 144 = 1369... 1
- In the following figure, point G, D, E, F are concyclic points of a circle with centre C. \(\angle ECF = 70^\circ\), \(m(\text{arc } DGF) = 200^\circ\). Find \(m(\text{arc } DE)\).[Figure: circle with centre C; D in the upper left, G in the upper rig… Answer: m(arc DE) = 90^° m(arc DGF) + m(arc DEF) = 360^° (the two arcs together make the complete circle). therefore m(arc DEF) = 360^° - 20... 1
- Find the distance between the points P (–1, 1) and Q (5, –7). Answer: d(P, Q) = 10 units By the distance formula, d(P, Q) = √((x₂ - x₁)² + (y₂ - y₁)²) = √((5 - (-1))² + (-7 - 1)²) = √(6² + (-8)²) = √(36... 1
- A person is standing at a distance of 80 m from a Church looking at its top. The angle of elevation is of 45º. Find the height of the Church.[Figure: right triangle with the church as the vertical side, the distance 80 m along the ground and the angl… Answer: height of the church = 80 m Let the height of the church be h metres and the distance of the person from its foot be 80 m. The trian... 1
- In the following figure, in \(\Delta ABC\) ray BD bisects \(\angle ABC\), A – D – C, seg ED \(\parallel\) side BC, A – E – B, then to prove that \(\dfrac{AB}{BC} = \dfrac{AE}{EB}\), complete the following activity.[Figure: \(\Delta ABC\) with A at th… Answer: (I) AB/BC = AD/DC ; (II) AE/EB = AD/DC , Basic proportionality theorem; therefore AB/BC = AE/EB . Activity completed: In Δ ABC , ray... 1
- If P is the midpoint of segment joining the points A (–4, 2) and B (6, 2), then complete the following activity to find the co-ordinates of point P.Activity : In the given example, suppose[Figure: A (–4, 2), P (x, y) and B (6, 2) are shown as three p… Answer: x = 1 and y = 2 , i.e. P(1, 2). Activity completed: x = x₁ + x₂/2 = (-4) + 6/2 = 2/2 , so x = 1 . y = y₁ + y₂/2 = 2 + 2/2 = 4/2 , so... 1
- In \(\Delta PQR\), point S is the midpoint of side QR. If PQ = 11, PR = 17, PS = 13, find QR. Answer: QR = 12 S is the midpoint of QR, so PS is a median of Δ PQR . By Apollonius' theorem, PQ² + PR² = 2PS² + 2QS² 11² + 17² = 2(13)² + 2... 1
- Prove that, opposite angles of a cyclic quadrilateral are supplementary. Answer: Proof — each pair of opposite angles of a cyclic quadrilateral adds up to 180^° . Given: square ABCD is a cyclic quadrilateral inscr... 1
- Draw a circle of radius 3.3 cm. Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at point P and Q. Write your observation about the tangents. Answer: Chord PQ (= 6.6 cm) is a diameter of the circle, so the tangents at P and Q are parallel to each other. Rough figure: a circle with... 1
- In the following figure if \(A(\text{P -- ABC}) = 154\) cm2, radius of the circle is 14 cm, find : (a) \(m\angle APC\), (b) \(l(\text{arc } ABC)\).[Figure: circle with centre P; A at the bottom of the circle, C at the right of the circle, B on the ar… Answer: (a) m∠ APC = 90^° ; (b) l(arc ABC) = 22 cm (a) Area of sector P–ABC = θ/360 × π r² (take π = 22/7 ) 154 = θ/360 × 22/7 × 14² = θ/360... 1
- In the following figure, line \(l\) intersects side AB and side AC of \(\Delta ABC\) in points P and Q respectively. Show that \(\dfrac{A(\Delta APQ)}{A(\Delta ABC)} = \dfrac{AP \times AQ}{AB \times AC}\).[Figure: \(\Delta ABC\) with A at the top, B… Answer: Proof by comparing areas of triangles with a common vertex. Given: line l intersects side AB at P and side AC at Q in Δ ABC . To pro... 1
- Find the number of coins of 2.2 cm diameter and 0.2 cm thick, can be made by melting a metallic right circular cylinder of height 0.2 m and diameter 8.8 cm. Answer: 1600 coins Height of the cylinder = 0.2 m = 20 cm; its radius = 8.8/2 = 4.4 cm. Volume of the cylinder = π r² h = π (4.4)² (20) = 38... 1
- AB is a chord of a circle with centre O. AC is a diameter of a circle. Line AT is a tangent at A. Write the answers of the following questions :(a) Draw the figure using the given information.(b) Find the measure of \(\angle CAT\).(c) Find the measur… Answer: (b) m∠ CAT = 90^° ; (c) m∠ ABC = 90^° . (a) Figure (as drawn): draw a circle with centre O. Draw diameter AC (A, O, C collinear). Ta... 1
- \(\alpha\) is acute angle. If \(3\sin\alpha - 4\cos\alpha = 0\), then find the values of \(\tan\alpha\) and \(\sec\alpha\). Answer: tanα = 4/3 and secα = 5/3 3sinα - 4cosα = 0 , so 3sinα = 4cosα . Dividing both sides by 3cosα (as α is acute, cosα ≠ 0 ): tanα = sin... 1
- In the following figure Δ ABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and AC are congruent. A circle touches the three sides of triangle as shown.Find the length of tangent segment from A to circle.[Figu… Answer: the tangent segment from A is 10 cm. AB = AC = 44 - 12/2 = 16 cm. Let the circle touch AB at P, AC at Q and BC at R. Tangent segment... 1
- Draw right-angled \(\Delta ABC\) of lengths of sides are 3 cm, 4 cm and 5 cm. Draw median on the hypotenuse of \(\Delta ABC\). Then :(i) Measure the length of median and write it.(ii) By observing lengths of median and hypotenuse write your observati… Answer: (i) the median on the hypotenuse is 2.5 cm (ii) the median drawn to the hypotenuse of a right-angled triangle is half of the hypoten... 1