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Chapter 9: Q12. (page 336)

Discover and prove a theorem about two lines tangent to a circle at the endpoints of a diameter.

Short Answer

Expert verified

Lines are parallel.

Step by step solution

01

Step 1. Given information.

Let a circle with centre O and diameter CD. Let MN be the tangent at point C and PQ be the tangent at point D.

02

Step 2. Formula used.

Tangent at any point of circle is perpendicular to the radius through point of contact.

03

Step 3. Proof.

Consider the figure below,

Here, MNis tangent at point C and PQis tangent at point D. Therefore,

OC⊥MNOD⊥PQ

Therefore,

∠OCN=90°∠ODQ=90°

i.e., ∠OCM=90∘and∠ODP=90°

For lines MNand PQand transversal AB, ∠DCM=∠CDQ,

both alternate angels are equal.

Therefore, lines are parallel.

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Most popular questions from this chapter

For each exercise draw a circle and inscribe the polygon in the circle.

c. An obtuse triangle.

For each exercise draw ⊙O with radius 12. Then draw radii OA¯ and to OB¯ form an angle with the measure named. Find the length of AB¯.

a. m∠AOB=90°

Name three radii of ⊙o.

Name a secant of the sphere and a chord of the sphere.

Given: PT¯is tangent to ⊙Oat T;TS¯⊥PO¯

Complete the following statements.

a. TS is the geometric mean between ? and ?

b. TO is the geometric mean between ? and ?

c. If OS=6 and SP=24,TS=? and TP=?
See all solutions

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