Tangent Perimeter Challenge
Use equal tangents to rebuild all three sides of a triangle.
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Choose a maths challenge
Pick a chapter and solve one complete problem. Every challenge explains the reasoning in small steps, just like the learning apps.
Hidden AP Term Challenge
Turn two known terms into equations and jump to a later term.
Start challengeFast Elimination Challenge
Match coefficients, eliminate one variable, and verify the pair.
Start challengeRemainder to HCF Challenge
Turn unequal remainders into exact divisibility before finding an HCF.
Start challengeReciprocal Zeroes Challenge
Convert a reciprocal expression into sum and product of zeroes.
Start challengeTwo Roots, Not One Challenge
Factor a difference of squares and keep both roots.
Start challengeMatch the Similar Triangles Challenge
Find missing angles and match vertices in the correct order.
Start challengeSection Formula Balance Challenge
Weight the opposite endpoint correctly in an internal ratio.
Start challengeProve One Side Challenge
Transform one side of an identity without assuming the result.
Start challengeObserver Height Challenge
Build the right triangle from eye level, then restore observer height.
Start challengeShaded Ring Challenge
Subtract the inner circle before substituting values.
Start challengeHidden Faces Challenge
Count only exposed surfaces when two solids are joined.
Start challengeFind the Median Class Challenge
Locate the halfway observation using cumulative frequency.
Start challengeNeither Event Challenge
Count the excluded outcomes once, then use the complement.
Start challengeClass 10 Board-Style Challenge: Exposed Surfaces
Decide which faces of three joined solids are actually exposed.
Start challengeWater Capacity Around a Solid Dome
Find how much water fits after a solid hemisphere takes up space inside a cylindrical glass.
Start challengeWater Height After Removing the Dome
Keep the same water volume while removing a solid hemisphere, then calculate its new height.
Start challengeTwo Circles and a Hidden Midpoint
Decide whether a common tangent is bisected by the tangent at the point of contact.
Start challengeThe Framed Photo Challenge
Find a photo dimension from its perimeter and the area change caused by a uniform border.
Start challengeTwo Inradii in a Right Triangle
Find the inradius of a right triangle from the inradii of its two altitude sub-triangles.
Start challengeThe Three Semicircles Challenge
Find the exact shaded area between three nested semicircles using only a perpendicular chord.
Start challengeThe Incircle Hypotenuse Split
Find the area of a right triangle from the two segments created on the hypotenuse by its incircle.
Start challengeThe Crossing Ropes Height Challenge
Find the crossing height of two ropes tied between two vertical poles when their separation distance is unknown.
Start challengeThe Concentric Circles Chord Trap
Two concentric circles of radii 5 cm and 3 cm: find the chord of the larger circle that touches the smaller one.
Start challengeThe 5 tan θ = 4 Shortcut Challenge
Given 5 tan θ = 4, evaluate a sin–cos ratio in seconds without drawing a triangle.
Start challengeThe Corner Sectors Decoy Challenge
A triangular park with sides 14 m, 20 m and 24 m has a 7 m sector at each corner. Find their total area.
Start challengeWhere Does the 30° Go? Angle of Depression Trap
From the top of a 75 m lighthouse the angle of depression of a boat is 30°. How far is the boat?
Start challengeCan HCF = 15 and LCM = 175?
Decide in seconds whether two numbers can have HCF 15 and LCM 175, without factorising.
Start challengeThe AP Sum Ratio to 11th Term Trap
Find the ratio of the 11th terms of two APs from the ratio of their sums of n terms.
Start challengeThe Triangles BPT vs Similarity Base Trap
DE is parallel to BC in triangle ABC. Find DE from AD, DB and BC.
Start challengeThe Parallel Tangents Right Angle Challenge
A tangent cuts two parallel tangents of a circle at A and B. Find the angle AOB at the centre.
Start challengeNo Angle Needed: tan θ + cot θ = 4
Given tan θ + cot θ = 4, find sec²θ + cosec²θ without ever finding θ.
Start challengeDivisible by 4 or 6, But Not Both
A number from 1 to 60 is picked at random. Find the probability that it is divisible by 4 or 6, but not both.
Start challengeThe Ratio Upside Down
Find the ratio in which the line 2x + y − 4 = 0 divides the segment joining A(2, −2) and B(3, 7).
Start challengeThe Number That Has a Twin
A two-digit number plus the number with its digits reversed is 66, and the digits differ by 2. Find the number.
Start challengeThe Hidden Term
If α and β are the zeroes of x² − p(x + 1) − c, show that (α + 1)(β + 1) = 1 − c.
Start challengeWant to explore before solving?
Read a short maths article, browse chapter guides, or visit the main Young Math Brains website.