...line joining the center of two intersecting circles bisects their common chord at right angles. 48. In the same circle or in equal circles, equal chords are equally distant from the center; and of two unequal chords, the shorter is farther from the center. 49. Converse of 48. 50. A tangent...

...also (?) (219). .-. OP is .L to AB at its midpoint (?) (70). IV. Arc AX = arc UK (?) (206). QED 221. THEOREM. In the same circle (or in equal circles) equal chords are equally distant from the center. Given : OO ; chord AB = chord CD, and distances OE and OF. To Prove : OE = OF. Proof : Draw radii OA...

...bisector of CD is the locus of all points equally distant from C and D. ... etc. THEOREM IX 258. In the same circle or in equal circles, equal chords are equally distant from the center; and of two unequal chords, the slwrter is farther from the center. Given: CD = EF and AB<EF in the...

...BC. (§ 155) 5. Again, ZAOD = ^BOD. (§41,2) 6. Then, arc AD = arc BD. (?) PROP. IX. THEOREM 164. In the same circle, or in equal circles, equal chords are equally distant from the centre. Draw a O with centre at O ; draw equal chords AB and CD. Draw lines OE and OF± AB and CD,...

...BC. (§ 155) 5. Again, ZAOD = ^BOD. (§41,2) 6. Then, arc AD = arc BD. (?) PROP. IX. THEOREM 164. In the same circle, or in equal circles, equal chords are equally distant from the centre. Draw a O with centre at O ; draw equal chords AB and CD. Draw lines OE and OF± AB and (7Z>,...

...line fulfils any two of the conditions, the remaining two are also fulfilled. PROPOSITION XXVIII 97. Theorem: In the same circle, or in equal circles, equal chords are equally distant from the center, and conversely. Assume that the distance from a point to a line is measured on the perpendicular from...

...third vertex if the triangle is fixed in size and shape? STRAIGHT LINES AND CIRCLES. 1O. Prone that in the same circle or in equal circles equal chords are equally distant from the center. SUGGESTION. MB = ND. Why? Then prove A BM C = A CND. 11. State and prove the converse of the theorem...

...third vertex if the triangle is fixed in size and shape? STRAIGHT LINES AND CIRCLES. 10. Prove that in the same circle or in equal circles equal chords are equally distant from the center. SUGGESTION. MB = ND. Why? Then prove A BMC ^ A CND. 11. State and prove the converse of the theorem...

...diameter perpendicular to a chord bisects the chord and its subtended arcs 261 • THEOREM LXI 249. In the same circle, or in equal circles, equal chords are equally distant from the centers 261 THEOREM LXII THEOREM LXV PAGE 256. Two parallels intercept equal arcs on a circumference...

...so as to form in each case an isosceles triangle with two given lines in the plane? 2. Prove that in the same circle, or in equal circles, equal chords are equally distant from the centre, and that of two unequal chords the less is at the greater distance from the centre. Two chords...