🔥 TRICKY GEOMETRY CHALLENGE! 🔥|| Class10th Triangle, circle & tangent related questions|| CBSE board

Описание: 🔥 TRICKY GEOMETRY CHALLENGE! 🔥
A triangle ABC is perfectly drawn around a circle of radius 4 cm, touching all three sides! The touch points divide the base BC into segments BD = 10 cm and DC = 8 cm.
But here’s the twist — the area of ΔABC is 90 cm²!
Your mission:
✨ Find the lengths of sides AB and AC!
This problem beautifully combines:
🔹 Properties of tangents drawn from external points
🔹 Incircle geometry
🔹 Area formula using semiperimeter (A = r × s)
🔹 Smart algebraic reasoning
Are you ready to crack this satisfying geometric puzzle?
More Attractive Description
💡 A triangle that hugs a circle!
With a radius of 4 cm, the incircle sits snugly inside ΔABC.
Base BC is split into 10 cm and 8 cm.
Given area = 90 cm², use geometry magic to reveal the hidden sides AB and AC.
Perfect for Class 10/11 geometry practice & competitive exams!
🌟 (Extended Version) 🌟
Dive into this mind-twisting geometry puzzle where a triangle and a circle fit together perfectly!
You are given a triangle ΔABC that circumscribes a circle of radius 4 cm — meaning every side of the triangle touches the circle.
The base BC is divided into two precise segments:
🔸 BD = 10 cm
🔸 DC = 8 cm
But the real challenge begins now…
The area of triangle ABC is 90 cm²!
Your task?
🧩 Find the lengths of sides AB and AC using incircle properties, tangent segments, and the powerful formula:
👉 Area = radius × semiperimeter
This problem checks your:
✔ Tangent-length concepts
✔ Understanding of incircles
✔ Use of semiperimeter
✔ Algebra + geometry fusion skills
Perfect for students preparing for:
🔥 CBSE Class 10 & 11 Boards
🔥 NTSE / Olympiad
🔥 School exams & practice worksheets
✨ Even More Detailed & Attractive Description ✨
Welcome to one of the most beautiful applications of incircle geometry!
Triangle ABC touches the circle at points D, E, F forming equal tangent pairs.
The base BC is split as:
💠 BD = 10 cm
💠 DC = 8 cm
Given area = 90 cm²,
Use the relationship:
⭐ A = r × s
Where r is the inradius (4 cm) and s is the semiperimeter.
From this, find the semiperimeter → total sides → then sides AB & AC using tangent pair relations.
A smart mix of logic & math!
Ideal for:
📘 Class 9 & 10 geometry
📘 CBSE 2026 exams
📘 Daily practice & concept strengthening
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