...CONVERSELY : In the same circle, or equal circles, if two chords are unequally distant from the centre, they are unequal, and the chord at the less distance is the greater. In the circle whose centre is O, let AB and CD be unequally distant from O; and let OK perpendicular...

...OH, or its equal OF, is greater than OG. PROPOSITION XIII. THEOREM. 167. (Converse of Prop. XII.) In the same circle, or in equal circles, if two chords are unequally distant from the centre, the more remote is the less. In the circle ABD, let chord AB be more remote from the centre...

...distance. 238. In the same circle, or equal circles, if two chords are unequally distant from the centre, they are unequal, and the chord at the less distance is the greater. 239. A straight line perpendicular to a radius at its extremity is a tangent to the circle. 240. Cor....

...Therefore AB is farther from the centre than CD. QED PROPOSITION XV. THEOREM. 166. CONVERSELY—In the same circle, or in equal circles, if two chords are unequally distant from the centre, the more remote is the less. Given—The chord AB in the circle ABD farther from the centre...

...But, OH>OK. And, OK > OG. (?) PROP. XIII. THEOREM. 167. (Converse of Prop. XII.) In the same cirde, or in equal circles, if two chords are unequally distant from the centre, the more remote is the less. Given 0 the centre of QABC, and chord AB more remote from 0 than...

...distance from 0 than c' is from 0'. [Gen. Ax. [Why? [? [§ 42 (4). [? PROPOSITION XXXII. THEOREM. 163. In equal circles, if two chords are unequally distant from the center, the one at less distance from the center is the greater chord. EXERCISES. 1. Through a given point...

...OH= OF. (§ 164) But, OH>OK. And, OK> OG. (?) PROP. XIII. THEOREM. 167. (Converse of Prop. XII.) In the same circle, or in equal circles, if two chords are unequally distant from, the centre, the more remote is the less. Given O the centre of OABC, and chord AB more remote from O than...

...< OH. § 153 . But OH = OF. § 249 .-.OE<OF. O..ED PROPOSITION VIII. THEOREM. 251. CONVERSELY : In the same circle or in equal circles, if two chords are unequally distant from the centre, they are unequal; and the chord at the less distance is the greater. tig_ In the circle whose...

...intersection. EM > EG. (?) EK>EM. (?) Much more is EK > EG. .-. EF>EG. (?) Proposition HO. Theorem. 143. In the same circle, or in equal circles, if two chords are unequally distant from the centre, the chord at the less distance is the greater. Use the indirect method. Ex. 258. The shortest...

...CONVERSELY : In the same circle or in equal circles, if two chords are unequally distant from the centre, they are unequal; and the chord at the less distance is the greater. In the circle whose centre is 0, let AB and CD be unequally distant from 0 ; and let OE, the perpendicular...