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### How to solve: \”BC is tangent to Circle A at B and to Circle D at C. AB = 10, BC = 12, and . . .\”

How to solve: \”BC is tangent to Circle A at B and to Circle D at C. AB = 10, BC = 12, and . . .\”

How to solve: \”BC is tangent to Circle A at B and to Circle D at C. AB = 10, BC = 12, and . . .\”

### Circle Geometry ^{[1]}

The Improving Mathematics Education in Schools (TIMES) Project. The Improving Mathematics Education in Schools (TIMES) Project

Lines and circles are the most elementary figures of geometry − a line is the locus of a point moving in a constant direction, and a circle is the locus of a point moving at a constant distance from some fixed point − and all our constructions are done by drawing lines with a straight edge and circles with compasses. Tangents are introduced in this module, and later tangents become the basis of differentiation in calculus.

They clearly need to be proven carefully, and the cleverness of the methods of proof developed in earlier modules is clearly displayed in this module. The logic becomes more involved − division into cases is often required, and results from different parts of previous geometry modules are often brought together within the one proof

### 8.2 Circle geometry ^{[2]}

In the circle with centre \(O\), \(OQ \perp PR\), \(OQ = 4\) units and \(PR=10\). The following terms are regularly used when referring to circles:

– Chord — a straight line joining the ends of an arc.. – Circumference — the perimeter or boundary line of a circle.

– Diameter — a special chord that passes through the centre of the circle. A diameter is a straight line segment from one point on the circumference to another point on the circumference that passes through the centre of the circle.

### Tangent segments drawn from an external point to a circle are congruent, prove this theorem. Complete the following activity.Given: □ To Prove: □ Proof: Draw radius AP and radius AQ and complete – Geo ^{[3]}

Tangent segments drawn from an external point to a circle are congruent, prove this theorem. Proof: Draw radius AP and radius AQ and complete the following proof of the theorem.

∴ seg DP ≅ seg DQ …..[Corresponding sides of congruent triangles]

### Chapter 3 from Textbook Mathematics Part 2 (solutions) for Class 10 MATH ^{[4]}

Mathematics Part Ii (solutions) Solutions for Class 10 Math Chapter 3 Circle are provided here with simple step-by-step explanations. These solutions for Circle are extremely popular among class 10 students for Math Circle Solutions come handy for quickly completing your homework and preparing for exams

You will also love the ad-free experience on Meritnation’s Mathematics Part Ii (solutions) Solutions. All Mathematics Part Ii (solutions) Solutions for class 10 Math are prepared by experts and are 100% accurate.

(2) What is the distance of point C from line AB? Why ?. (1) It is given that line AB is tangent to the circle at A.

### Tangent to a Circle ^{[5]}

A line that touches the circle at a single point is known as a tangent to a circle. The point where tangent meets the circle is called point of tangency

Since tangent is a line, hence it also has its equation. In this article, we will discuss the general equation of a tangent in slope form and also will solve an example to understand the concept.

Point of tangency is the point at which tangent meets the circle. Now, let’s prove tangent and radius of the circle are perpendicular to each other at the point of contact.

### [Solved] Line AC is a tangent to a circle at point B on it, and PQ is ^{[6]}

Line AC is a tangent to a circle at point B on it, and PQ is a chord of the circle such that BP = BQ. Tangent chord theorem – The angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.

⇒ ∠PQB + ∠BPQ + ∠PBQ = 180° [Angle sum property of a triangle]. This is the provisional answer key and objections against the same can be submitted by 22nd August 2023

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### Sources

- https://amsi.org.au/teacher_modules/Circle_Geometry.html
- https://www.siyavula.com/read/za/mathematics/grade-11/euclidean-geometry/08-euclidean-geometry-02
- https://www.shaalaa.com/question-bank-solutions/tangent-segments-drawn-from-an-external-point-to-a-circle-are-congruent-prove-this-theorem-complete-the-following-activitygiven-to-prove-proof-draw-radius-ap-and-radius-aq-and-complete-tangent-segment-theorem_206628
- https://www.meritnation.com/maharashtra-class-10/math/mathematics_part_-_ii_(solutions)/circle/textbook-solutions/91_1_3385_24435_55_136441
- https://byjus.com/maths/tangent-to-a-circle/
- https://testbook.com/question-answer/line-ac-is-a-tangent-to-a-circle-at-point-b-on-it–61ee8a208afc9f57c64b46a9