ICSE Class 10CISCE
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Circles with Centres P and Q Intersect at Points a and B as Shown in Figure. Cbd is a Segment and Ebm is Tangent to the Circle with Centre Q, at Point B. If the Circle Are Congruent; Show that Ce = Bd - ICSE Class 10 - Mathematics

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ConceptTangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments

Question

Circles with centres P and Q intersect at points A and B as shown in the figure. CBD is a segment and EBM is tangent to the circle with centre Q, at point B. If the circle are congruent; show that
CE = BD

Solution

Join AB and AD
EBM is a tangent and BD is a chord.
`∠`DBM = `∠`BAD (angles in alternate segments)
But, `∠`DBM = `∠` CBE (Vertically opposite angles)
∴ `∠`BAD = `∠`CBE
Since in the same circle or congruent circles, if angles are equal, then chords opposite to them are also equal.
Therefore, CE = BD

 

 

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Solution Circles with Centres P and Q Intersect at Points a and B as Shown in Figure. Cbd is a Segment and Ebm is Tangent to the Circle with Centre Q, at Point B. If the Circle Are Congruent; Show that Ce = Bd Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.
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