Geometry, Triangles & Circles
Practice 400+ official SSC CGL Geometry PYQs online. Incenter angle 90 + A/2, circumcenter, cyclic quadrilaterals, tangents & 4-step solutions.
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4-Step Solution & Tricks
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🎯 High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Geometry, Triangles & Circles:
- Incenter & Angle Bisector Theorem (∠BIC = 90° + ∠A/2)
- Circumcenter & Central Angle Theorem (∠BOC = 2 ∠A)
- Centroid & Median 2:1 Ratio & Apollonius Theorem
- Circles: Tangent-Secant Theorem (PT² = PA · PB)
- Direct Common Tangent (DCT = √(d² - (r₁ - r₂)²)) & TCT
⚡ Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Geometry questions in under 45 seconds:
Incenter Angle: ∠BIC = 90° + A/2. Excenter Angle: ∠BEC = 90° - A/2.
Direct Common Tangent: DCT = √(d² - (r₁ - r₂)²).
Transverse Common Tangent: TCT = √(d² - (r₁ + r₂)²).
📖 Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
💡 View Step-by-Step Solution & Answer
Correct Answer: Equal to AX
- Step 1: DBC O E F A X Let O be a point inside the triangle.
- Step 2: OD ⊥ BC, OE ⊥ AC And OF ⊥ AB AB = BC = CA Area of (∆OAB + ∆OBC + ∆OAC ) = Area of ∆ABC ⇒ 1 2 1 2 1 2AB OF BC OD AC OE×+ ×+ ×× =× ×1 2 BC AX ⇒ OF OD OE AX++ =
⚡ Speed Tip: Verify intermediate calculations and units.
💡 View Step-by-Step Solution & Answer
Correct Answer: 10 3 3
- Step 1: Understand problem conditions and equations.
- Step 2: DBC E F G A BD = DC = 5 cm ∠ADB = 90° AB2 = BD2 + AD2 ⇒ 102 = 52 + AD2 ⇒ 100 = 25 + AD2 ⇒ AD2 = 100 – 25 = 75 ∴ AD == 75/53 ∴ AG AD== ×=2 3 2 3/53 10 3 3 cm
- Step 3: Evaluating gives verified answer: 10 3 3.
⚡ Speed Tip: Verify intermediate calculations and units.
💡 View Step-by-Step Solution & Answer
Correct Answer: 5 AD2
- Step 1: Understand problem conditions and equations.
- Step 2: D A BC AD ⊥ BC ∴ BD = DC AD AB BC AC===3 2 3 2 3 2 ⇒ AB AD BC AC== =2 3 ∴ AB2 + BC2 + AC2 =+ + =4 3 4 3 4 3 422AD AD
- Step 3: Evaluating gives verified answer: 5 AD2.
⚡ Speed Tip: Verify intermediate calculations and units.
❓ Frequently Asked Questions (FAQs)
What is the relation between Incenter angle and Vertex angle?
∠BIC = 90° + (∠A / 2). If vertex angle is 60°, incenter angle is 90° + 30° = 120°.