In ▢ABCD points P, Q, R and S lies on sides AB, BC, CD and AD respectively such that seg PS is parallel to seg BD parallel to seg QR and seg PQ is parallel to seg SR. Then prove that seg PQ is parallel to seg AC. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
In △ABC, m∠BAC=90°. Seg DE is perpendicular to side AB, seg DF is perpendicular to AC. Prove that Area of quadrilateral AEDF= √(AE x EB x AFx FC) Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
In △BAC, Angle BAC= 90°, segment AD, seg BE and seg CF are medians. Prove: 2(AD²+BE²+CF²)=3BC² Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
Find the radius of a circle drawn by a compass when angle between two arms of compass is 120° and length of each arm is 24cm. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
In △PQR, angle PQR= 90°, As shown in figure, seg QS is perpendicular to side PR. Seg QM is angle bisector of angle PQR. Prove that: PM²/MR² = PS/SR. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
Bisector of angle B and angle C in △ABC meet each other at P. Line AP cuts the side BC at Q. Prove that: AP/PQ=(AB+AC)/BC. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
Through the midpoint M of the side CD of parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL=2BL. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
In Quadrilateral ABCD, M is the midpoint of diagonal AC and N is the midpoint of diagonal BD. Prove that: AB²+BC²+CD²+DA²=AC²+BD²+4MN². Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
△PQR is a right angled at Q such that QR=b and a=A(△PQR). If QN is perpendicular to PR then S.T: QN = 2ab/√(b^4+4a²) Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
In △ABC, angle ABC= 135°. Prove that AC² = AB² + BC² + 4A(△ABC). Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
In the adjoining figure, each of segments PA, QB, RC and SD is perpendicular to line l. If AB=6, BC=9 , CD=12 and PS=36, then determine PQ, QR and RS. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
In an equilateral triangle ABC, the side BC is trisected at D. Prove that 9AD² = 7AB². Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
In triangle ABC, Angle ACB=90°, seg CD is perpendicular to seg AB, seg DE is perpendicular to seg CD. Show that: CD² x AC = AD x AB x DE. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
In the adjoining figure, AD is the bisector of the exterior angle A of triangle ABC. Seg AD intersects the side BC produced in D. Prove that: BD/CD=AB/AC. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
In Quadrilateral ABCD, side BC is parallel to side AD. Side AC and side BD intersect in point Q. If AQ=(1/3)AC then show that, DQ=(1/2)BQ. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
Solve: 216x^6 - 793x^3 + 216 = 0 Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
A man travels by boat 36 km down a river and back in 8 hours. If the speed of his boat in still water is 12 km per hour, find the speed of the river current. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
If the sum of the roots of the quadratic equation ax²+bx+c=0 is equal to the sum of the squares of their reciprocals. Show that bc², ca², ab² are in A.P. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
Find the value of p, if the equations 3x²-2x+p=0 and 6x²-17x+12=0 have a common root. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
Find the condition that the equations ax²+bx+c=0 and a1x²+b1x+c1=0 may have a common root. Find this common root, when it exists Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
From the quadratic equation whose roots are the squares of the sum of roots and square of the difference of roots of the equation 2x²+2x(m+n)+m²+n²=0. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
If the sum of the roots of the quadratic equation ax²+bx+c=0 is equal to the sum of the squares of their reciprocals then, Prove that: 2a²c= c²b + b²a. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
If the roots of the quadratic equation ax²+bx+c=0 are in the ration p:q. Show that √(p/q)+√(q/p)+√(c/a) = 0. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
A businessman bought some items for Rs. 600, keeping 10 items for himself he sold the remaining items at a profit of Rs. 5 per item. From the amount received in this deal he could buy 15 more items. Find the original price of each item. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
One tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
Tinu takes 9 days more than his father to do a certain piece of work. Together they can do the work in 6 days. How many days tinu take to do that work. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
An express train takes 30 min less for a journey of 440 km, if its usual speed is increased by 8 km/hr. Find its usual speed. Get link Facebook Twitter Pinterest Email Other Apps September 30, 2018 Read more
