**Q.29 Cash Award Qn posted on 01.09.2024**

**Q.28 Cash Award Math Rider posted on 01.08.2024 **

**Q.27 Cash Award Math Rider posted on 01.07.2024 **

**Q.26 Cash Award Math Rider posted on 01.06.2024**

**Q.25 Cash Award Qn posted on 01.05.2024**

**Q.24 Cash Award Qn posted on 01.04.2024**

**Q.23 Cash Award Math Rider posted on 01.03.2024**

**Q.22 Cash Award Math Rider posted on 01.02.2024**

**Q.21 Cash Award Qn posted on 01.01.2024**

**Q.20 Cash Award Math Rider posted on 01.12.2023**

**Q.19 Cash Award Qn posted on 01.11.2023**

**Q.18 Cash Award Qn posted on 01.10.2023**

**Q.17 Cash Award Qn posted on 01.09.2023**

**Q.16 Cash Award Qn posted on 01.08.2023**

**Q.15 Cash Award Qn posted on 01.07.2023**

**Q.14 Cash Award Qn posted on 01.06.2023**

**Q.13 Cash Award Qn posted on 01.05.2023**

**Q.12 Cash Award Qn posted on 01.04.2023**

In the picture, ABCD is a cyclic quadrilateral and BD is its diagonal. AE, AR & AM are respectively the altitude, angle bisector and median of triangle ABD. Similarly, CF, CS & CM are respectively the altitude, angle bisector & median of triangle CBD. Given that AE = CF. Prove: (MS^2-MR^2) = (FS^2-ER^2).

** Question created byDr.M.Raja Climax,
Founder Chairman, CEOA**

**Q.11 Cash Award Qn posted on 01.03.2023**

In âˆ† ABC, AB = 10 units and AD is the altitude. âˆ DAC=30Â°. E is a point on AB produced such that BE = 2 units. ED is joined and produced to meet AC at F and DF is found to be 5 units. Prove : AF = 2FC.

** Question created byDr.M.Raja Climax,
Founder Chairman, CEOA**

**Q.10 Cash Award Qn posted on 01.02.2023**

**Q.9 Cash Award Qn posted on 01.01.2023**

In the picture, O is the centre of the circle, AB is a chord and M is its midpoint. CD is another chord passing through M as shown in the picture and DF is the diameter. The perpendicular line drawn from C to AB meets the other side of the circle at E as shown in the picture.

Prove : The measurements of EM, DM & FC will constitute the sides of a right triangle.

** Question created by
Dr.M.Raja Climax
Founder Chairman, CEOA Institutions**

**Q.8 Cash Award Qn posted on 01.12.2022**

In the picture, two circles (one small and one big) intersect each other at A & B. C is any point on the major arc AB of the smaller circle. AC & BC are joined and produced to meet the bigger circle at D & E respectively. M & N are points on minor arcs AC & BC respectively of smaller circle such that CE = CM and CD = CN. AN & BM intersect at O. CP âŠ¥ AN and CQ âŠ¥ BM are drawn. Prove: OP = OQ

** Question created by
Dr.M.Raja Climax
Founder Chairman, CEOA Institutions**

**Q.7 Cash Award Qn posted on 01.10.2022**

###### 01.10.2022 -FESTIVAL MONTH BUMPER PRIZE RIDER

ABCD is a cyclic quadrilateral where AB > AD and CB = CD. AC & BD cutat O. CE is drawn perpendicular to AB. M is the midpoint of BD. EM is joined and produced to meet AC & AD produced at N and G respectively.

Prove: AO = EM X MG/CN

** Question created by
Dr.M.Raja Climax
Founder Chairman, CEOA Institutions**

**Q.6 Cash Award Qn posted on 01.09.2022**

In the adjoining picture, AD & BE are altitudes of △ABC and O is the orthocentre. F is a point on BE produced such that OE = EF. DE & CF meet at G. Prove: BC/GC = FC/DC

** Question created by Dr.M.Raja Climax Founder Chairman, CEOA Institutions**

**Q.5 Cash Award Qn posted on 01.08.2022**

In the adjoining figure, AE: AC: BC= 1:9: 12, D is the mid-point of BC and AF=ED.

Find GB : BC. A

** Question created by
Dr.M.Raja Climax
Founder Chairman, CEOA Institutions**

**Q.4 Cash Award Qn posted on 01.07.2022**

For triangle ABC, AD is a median with AD = BC and Ois the circumcentre. OE is perpendicular to AD. CE is joined and produced to meet AB at F.

Prove: CE/EF = 11/5.

** Question created by
Dr.M.Raja Climax
Founder Chairman, CEOA Institutions**

**Q.3 Cash Award Qn posted on 01.06.2022**

ABCD is a quadrilateral with BC = CD and AB > AD. The diagonal AC is also the internal bisector of ZBAD. CE is drawn perpendicular to AB. M is the midpoint of BD. EM is joined and produced to meet CD at F.

Prove that BM = CExFM / FC

** Question created by
Dr.M.Raja Climax
Founder Chairman, CEOA Institutions**

**Q.2 Cash Award Qn posted on 01.05.2022**

ABC is an equilateral triangle ioeribed ina eircle.Disa point on minor arc BC.
AC & BD are produced to meet at E. AB & CD are produced to meet at F.
**Prove that AD ^{2 }= (BD*DE) + (CD*DF)**

**Q.1 Cash Award Qn posted on 31.03.2022**

In triangle ABC, BD is a median with G, the Centroid on it. M is the midpoint of GD. P is a point on AD such that AP = 2PD. AM is joined and produced to meet GC at N. PN is joined and produced to meet BC at Land ALis joined to cut GM at O. prove that BO = 40D.

** Question created by
Dr.M.Raja Climax
Founder Chairman, CEOA**