Math Problem Statement

The diagram shows the circle with equation x^2 + y^2 = 20. Tangents touching the circle at points B and C pass through the point A (0, 10). (a) By letting the equation of a tangent be y = mx + 10, find the two possible values of m. (b) Find the coordinates of B and C. (c) Find angle BDC in degrees.

Solution

Let's solve the questions step-by-step from the provided image.

Given:

The circle has the equation: x2+y2=20x^2 + y^2 = 20 with tangents touching the circle at points BB and CC passing through the point A(0,10)A(0, 10).

Question (a):

By letting the equation of a tangent be y=mx+10y = mx + 10, find the two possible values of mm.

To find the values of mm, we

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Circle Equations
Tangents
Slope and Angle Calculation

Formulas

Circle equation x^2 + y^2 = r^2
Tangent line equation y = mx + c
Slope of a line = (y2 - y1) / (x2 - x1)
Angle between lines formula: tan(θ) = |(m1 - m2) / (1 + m1*m2)|

Theorems

Tangent-Secant Theorem
Pythagorean Theorem

Suitable Grade Level

Grades 10-12

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